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@book{beer2015advancedbook,
  title={Advanced Numerical Simulation Methods: From CAD Data Directly to Simulation Results},
  author={Beer, Gernot},
  year={2015},
  publisher={CRC Press}
}

@article{HierarchicalBSplines1,
 author = {Forsey, David R. and Bartels, Richard H.},
 title = "{Hierarchical B-spline Refinement}",
 journal = {SIGGRAPH Comput. Graph.},
 issue_date = {Aug. 1988},
 volume = {22},
 number = {4},
 month = jun,
 year = {1988},
 issn = {0097-8930},
 pages = {205--212},
 numpages = {8},
 url = {http://doi.acm.org/10.1145/378456.378512},
 doi = {10.1145/378456.378512},
 acmid = {378512},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {free-form surface editing, refinement, splines, subdivision},
}

@article{HierarchicalBSplines2,
title = "A hierarchical approach to adaptive local refinement in isogeometric analysis ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "200",
number = "49–52",
pages = "3554 - 3567",
year = "2011",
note = "",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2011.09.004",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511002933",
author = "A.-V. Vuong and C. Giannelli and B. J{\"u}ttler and B. Simeon",
keywords = "Adaptivity",
keywords = "Isogeometric analysis",
keywords = "Hierarchical B-splines",
keywords = "Local refinement ",
abstract = "Adaptive local refinement is one of the key issues in isogeometric analysis. In this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical B-splines. We investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity. Furthermore, we use concepts well-established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting. This also allows us to access a posteriori error estimation techniques. Numerical results for several different examples are given and they turn out to be very promising. "
}

@article{THB0,
title = "{THB-splines: The truncated basis for hierarchical splines}",
journal = "Computer Aided Geometric Design",
volume = "29",
number = "7",
pages = "485 - 498",
year = "2012",
note = "",
issn = "0167-8396",
doi = "http://dx.doi.org/10.1016/j.cagd.2012.03.025",
url = "http://www.sciencedirect.com/science/article/pii/S0167839612000519",
author = "Carlotta Giannelli and Bert J{\"u}ttler and Hendrik Speleers",
keywords = "Hierarchical tensor–product B-splines",
keywords = "Truncated basis",
keywords = "Local refinement",
keywords = "Partition of unity"
}

@ARTICLE{THB1,
author={Giannelli, C. and J{\"u}ttler, B. and Kleiss, S.K. and Mantzaflaris, A. and Simeon, B. and Špeh, J.},
title="{THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis}",
journal={Computer Methods in Applied Mechanics and Engineering},
year={2016},
volume={299},
pages={337-365},
doi={10.1016/j.cma.2015.11.002},
note={cited By 4},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-84949034754&doi=10.1016%2fj.cma.2015.11.002&partnerID=40&md5=99a1f7fb1940ca878dced678e4666681},
document_type={Article},
source={Scopus},
}

@ARTICLE{THB2,
author={Hofreither, C. and J{\"u}ttler, B. and Kiss, G. and Zulehner, W.},
title={Multigrid methods for isogeometric analysis with THB-splines},
journal={Computer Methods in Applied Mechanics and Engineering},
year={2016},
volume={308},
pages={96-112},
doi={10.1016/j.cma.2016.05.005},
note={cited By 0},
url={https://www.scopus.com/inward/record.uri?eid=2-s2.0-84971634621&doi=10.1016%2fj.cma.2016.05.005&partnerID=40&md5=22ce1462aa500ce91774f2d5b1b4885f},
document_type={Article},
source={Scopus},
}
@article{moumnassi2014analysis,
  title={Analysis using higher-order XFEM: implicit representation of geometrical features from a given parametric representation},
  author={Moumnassi, Mohammed and Bordas, Stephane Pierre Alain and Figueredo, R{\'e}mi and Sansen, Pascal},
  journal={Mechanics \& Industry},
  volume={15},
  number={5},
  pages={443--448},
  year={2014},
  publisher={EDP Sciences}
}

@article{moumnassi2011finite,
	Author = {Moumnassi, Mohammed and Belouettar, Salim and B{\'e}chet, {\'E}ric and Bordas, St{\'e}phane PA and Quoirin, Didier and Potier-Ferry, Michel},
	Date-Added = {2017-04-13 10:58:44 +0000},
	Date-Modified = {2017-04-13 10:58:44 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Number = {5},
	Pages = {774--796},
	Publisher = {Elsevier},
	Title = {Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces},
	Volume = {200},
	Year = {2011}}
@article{parvizian2007finite,
  title={Finite cell method},
  author={Parvizian, Jamshid and D{\"u}ster, Alexander and Rank, Ernst},
  journal={Computational Mechanics},
  volume={41},
  number={1},
  pages={121--133},
  year={2007},
  publisher={Springer}
}

@article{moes2003computational,
	Author = {Mo{\"e}s, Nicolas and Cloirec, Mathieu and Cartraud, Patrice and Remacle, J-F},
	Date-Added = {2017-04-13 10:57:48 +0000},
	Date-Modified = {2017-04-13 10:57:48 +0000},
	Journal = {Computer methods in applied mechanics and engineering},
	Number = {28},
	Pages = {3163--3177},
	Publisher = {Elsevier},
	Title = {A computational approach to handle complex microstructure geometries},
	Volume = {192},
	Year = {2003}}

@article{belytschko2003structured,
	Author = {Belytschko, Ted and Parimi, Chandu and Mo{\"e}s, Nicolas and Sukumar, N and Usui, Shuji},
	Date-Added = {2017-04-13 10:56:01 +0000},
	Date-Modified = {2017-04-13 10:56:01 +0000},
	Journal = {International journal for numerical methods in engineering},
	Number = {4},
	Pages = {609--635},
	Publisher = {Wiley Online Library},
	Title = {Structured extended finite element methods for solids defined by implicit surfaces},
	Volume = {56},
	Year = {2003}}

@article{cirak2000subdivision,
	Author = {Cirak, Fehmi and Ortiz, Michael and Schroder, Peter},
	Date-Added = {2017-04-13 10:54:35 +0000},
	Date-Modified = {2017-04-13 10:54:35 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {12},
	Pages = {2039--2072},
	Title = {Subdivision surfaces: a new paradigm for thin-shell finite-element analysis},
	Volume = {47},
	Year = {2000}}

@article{cirak2011subdivision,
	Author = {Cirak, Fehmi and Long, Quan},
	Date-Added = {2017-04-13 10:52:34 +0000},
	Date-Modified = {2017-04-13 10:52:34 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {9},
	Pages = {897--923},
	Publisher = {Wiley Online Library},
	Title = {Subdivision shells with exact boundary control and non-manifold geometry},
	Volume = {88},
	Year = {2011}}

@article{legrain2013nurbs,
	Author = {Legrain, Gr{\'e}gory},
	Date-Added = {2017-04-13 10:51:48 +0000},
	Date-Modified = {2017-04-13 10:51:48 +0000},
	Journal = {Computational Mechanics},
	Number = {4},
	Pages = {913--929},
	Publisher = {Springer},
	Title = {A NURBS enhanced extended finite element approach for unfitted CAD analysis},
	Volume = {52},
	Year = {2013}}

@article{kagan1998new,
	Author = {Kagan, Pavel and Fischer, Anath and Bar-Yoseph, Pinhas Z},
	Date-Added = {2017-04-13 10:51:21 +0000},
	Date-Modified = {2017-04-13 10:51:21 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {3},
	Pages = {435--458},
	Publisher = {Wiley Online Library},
	Title = {New B-Spline Finite Element approach for geometrical design and mechanical analysis},
	Volume = {41},
	Year = {1998}}

@article{sevilla20113d,
	Author = {Sevilla, Ruben and Fern{\'a}ndez-M{\'e}ndez, Sonia and Huerta, Antonio},
	Date-Added = {2017-04-13 10:41:05 +0000},
	Date-Modified = {2017-04-13 10:41:05 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {2},
	Pages = {103--125},
	Publisher = {Wiley Online Library},
	Title = {3D NURBS-enhanced finite element method (NEFEM)},
	Volume = {88},
	Year = {2011}}

@article{sevilla2011nurbs,
	Author = {Sevilla, Ruben and Fern{\'a}ndez-M{\'e}ndez, Sonia and Huerta, Antonio},
	Date-Added = {2017-04-13 10:40:56 +0000},
	Date-Modified = {2017-04-13 10:40:56 +0000},
	Journal = {Archives of Computational Methods in Engineering},
	Number = {4},
	Pages = {441--484},
	Publisher = {Springer},
	Title = {NURBS-enhanced finite element method (NEFEM)},
	Volume = {18},
	Year = {2011}}

@article{sevilla2008nurbs,
	Author = {Sevilla, Ruben and Fern{\'a}ndez-M{\'e}ndez, Sonia and Huerta, Antonio},
	Date-Added = {2017-04-13 10:40:47 +0000},
	Date-Modified = {2017-04-13 10:40:47 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {1},
	Pages = {56--83},
	Publisher = {Wiley Online Library},
	Title = {NURBS-enhanced finite element method (NEFEM)},
	Volume = {76},
	Year = {2008}}

@article{wall2008isogeometric,
	Author = {Wall, Wolfgang A and Frenzel, Moritz A and Cyron, Christian},
	Date-Added = {2017-04-13 10:38:20 +0000},
	Date-Modified = {2017-04-13 10:38:20 +0000},
	Journal = {Computer methods in applied mechanics and engineering},
	Number = {33},
	Pages = {2976--2988},
	Publisher = {Elsevier},
	Title = {Isogeometric structural shape optimization},
	Volume = {197},
	Year = {2008}}

@article{seo2010shape,
	Author = {Seo, Yu-Deok and Kim, Hyun-Jung and Youn, Sung-Kie},
	Date-Added = {2017-04-13 10:04:37 +0000},
	Date-Modified = {2017-04-13 10:04:37 +0000},
	Journal = {International Journal of Solids and Structures},
	Number = {11},
	Pages = {1618--1640},
	Publisher = {Elsevier},
	Title = {Shape optimization and its extension to topological design based on isogeometric analysis},
	Volume = {47},
	Year = {2010}}

@article{buffa2010isogeometric,
	Author = {Buffa, Annalisa and Sangalli, Giancarlo and V{\'a}zquez, Rafael},
	Date-Added = {2017-04-13 10:04:23 +0000},
	Date-Modified = {2017-04-13 10:04:23 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Number = {17},
	Pages = {1143--1152},
	Publisher = {Elsevier},
	Title = {Isogeometric analysis in electromagnetics: B-splines approximation},
	Volume = {199},
	Year = {2010}}

@article{de2011x,
	Author = {De Luycker, E and Benson, DJ and Belytschko, T and Bazilevs, Y and Hsu, MC},
	Date-Added = {2017-04-13 10:03:53 +0000},
	Date-Modified = {2017-04-13 10:03:53 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {6},
	Pages = {541--565},
	Publisher = {Wiley Online Library},
	Title = {X-FEM in isogeometric analysis for linear fracture mechanics},
	Volume = {87},
	Year = {2011}}

@article{lian2013stress,
	Author = {Lian, Haojie and Simpson, Robert N and Bordas, St{\'e}phane},
	Date-Added = {2017-04-13 09:56:34 +0000},
	Date-Modified = {2017-04-13 09:56:34 +0000},
	Journal = {Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics},
	Number = {2},
	Pages = {88--99},
	Title = {Stress analysis without meshing: Isogeometric boundary-element method},
	Volume = {166},
	Year = {2013}}

@article{lian2017shape,
	Author = {Lian, Haojie and Kerfriden, P and Bordas, SPA},
	Date-Added = {2017-04-13 09:54:35 +0000},
	Date-Modified = {2017-04-13 09:54:35 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {1--41},
	Publisher = {Elsevier},
	Title = {Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines},
	Volume = {317},
	Year = {2017}}

@article{lian2012recent,
	Author = {Lian, Haojie and Bordas, SPA and Sevilla, Rub{\'e}n and Simpson, RN},
	Date-Added = {2017-04-13 09:54:03 +0000},
	Date-Modified = {2017-04-13 09:54:03 +0000},
	Journal = {arXiv preprint arXiv:1210.8216},
	Title = {Recent developments in CAD/analysis integration},
	Year = {2012}}

@article{lian2015implementation,
	Author = {Lian, Haojie and Kerfriden, Pierre and Bordas, Stephane Pierre Alain},
	Date-Added = {2017-04-13 09:53:37 +0000},
	Date-Modified = {2017-04-13 09:53:37 +0000},
	Journal = {International Journal for Numerical Methods in Engineering},
	Publisher = {Wiley Online Library},
	Title = {Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity},
	Year = {2015}}

@article{xuan2016isogeometric,
	Author = {Xuan, PENG},
	Date-Added = {2017-04-13 09:52:47 +0000},
	Date-Modified = {2017-04-13 09:52:47 +0000},
	Title = {Isogeometric boundary element methods for linear elastic fracture mechanics},
	Year = {2016}}

@article{peng2016linear,
	Author = {Peng, Xuan and Atroshchenko, Elena and Kerfriden, Pierre and Bordas, SPA},
	Date-Added = {2017-04-13 09:52:32 +0000},
	Date-Modified = {2017-04-13 09:52:32 +0000},
	Journal = {International Journal of Fracture},
	Pages = {1--24},
	Publisher = {Springer},
	Title = {Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment},
	Year = {2016}}

@inproceedings{peng2014damage,
	Author = {Peng, Xuan and Atroshchenko, Elena and Bordas, St{\'e}phane},
	Booktitle = {Proc. sixth international conference on advanced computational methods in engineering},
	Date-Added = {2017-04-13 09:52:17 +0000},
	Date-Modified = {2017-04-13 09:52:17 +0000},
	Title = {Damage tolerance assessment directly from CAD:(extended) isogeometric boundary element methods (XIGABEM)},
	Year = {2014}}

@article{peng2017isogeometric,
	Author = {Peng, Xuan and Atroshchenko, Elena and Kerfriden, Pierre and Bordas, SPA},
	Date-Added = {2017-04-13 09:52:02 +0000},
	Date-Modified = {2017-04-13 09:52:02 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {151--185},
	Publisher = {Elsevier},
	Title = {Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth},
	Volume = {316},
	Year = {2017}}

@article{marussig2015fast,
	Author = {Marussig, Benjamin and Zechner, J{\"u}rgen and Beer, Gernot and Fries, Thomas-Peter},
	Date-Added = {2017-04-13 09:39:08 +0000},
	Date-Modified = {2017-04-13 09:39:08 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {458--488},
	Publisher = {Elsevier},
	Title = {Fast isogeometric boundary element method based on independent field approximation},
	Volume = {284},
	Year = {2015}}

@article{beer2017isogeometric,
	Author = {Beer, Gernot and Mallardo, Vincenzo and Ruocco, Eugenio and Marussig, Benjamin and Zechner, J{\"u}rgen and D{\"u}nser, Christian and Fries, Thomas-Peter},
	Date-Added = {2017-04-13 09:38:40 +0000},
	Date-Modified = {2017-04-13 09:38:40 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {418--433},
	Publisher = {Elsevier},
	Title = {Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 2: 3-D problems},
	Volume = {315},
	Year = {2017}}

@article{beer2016advanced,
	Author = {Beer, Gernot and Duenser, Christian},
	Date-Added = {2017-04-13 09:38:30 +0000},
	Date-Modified = {2017-04-13 09:38:30 +0000},
	Journal = {Computers and Geotechnics},
	Pages = {86--95},
	Publisher = {Elsevier},
	Title = {Advanced Boundary Element analysis of geotechnical problems with geological inclusions},
	Volume = {79},
	Year = {2016}}

@article{beer2016isogeometric,
	Author = {Beer, Gernot and Marussig, Benjamin and Zechner, J{\"u}rgen and D{\"u}nser, Christian and Fries, Thomas-Peter},
	Date-Added = {2017-04-13 09:38:00 +0000},
	Date-Modified = {2017-04-13 09:38:00 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {552--570},
	Publisher = {Elsevier},
	Title = {Isogeometric Boundary Element analysis with elasto-plastic inclusions. Part 1: Plane problems},
	Volume = {308},
	Year = {2016}}

@article{beer2015simple,
	Author = {Beer, Gernot and Marussig, Benjamin and Zechner, J{\"u}rgen},
	Date-Added = {2017-04-13 09:37:48 +0000},
	Date-Modified = {2017-04-13 09:37:48 +0000},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {776--790},
	Publisher = {Elsevier},
	Title = {A simple approach to the numerical simulation with trimmed CAD surfaces},
	Volume = {285},
	Year = {2015}}

@article{beer2014boundary,
	Author = {Beer, Gernot and Marussig, Benjamin and Zechner, J{\"u}rgen and D{\"u}nser, Christian and Fries, Thomas-Peter},
	Date-Added = {2017-04-13 09:37:30 +0000},
	Date-Modified = {2017-04-13 09:37:30 +0000},
	Journal = {arXiv preprint arXiv:1406.3499},
	Title = {Boundary Element Analysis with trimmed NURBS and a generalized IGA approach},
	Year = {2014}}

@article{Nguyen2016,
	Abstract = {The isogeometric analysis is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyze quasi-static elastic problems including crack problems in two-dimensional domains. This method takes the advantages from the common boundary representation of the isogeometric analysis and the boundary element method. The background of the developed method is to use non-uniform rational B-splines (NURBS) for the Galerkin approximation of both geometry and field variables (i.e.the displacement and traction on the boundary). The basic ingredient of the method is a pair of weakly-singular weak-form integral equations for the displacement and traction on the boundary. These integral equations contain at most weakly-singular kernels of lnr, where r is the distance from a source point to a field point. Various numerical examples are examined to validate the accuracy and efficiency of the proposed method. A model of crack propagation is also discussed to illustrate the use of the method for crack growth simulation. Through the numerical examples, it is observed that the isogeometric SGBEM produces highly accurate results yet it is simple to implement.},
	Author = {Nguyen, BH and Tran, HD and Anitescu, C and Zhuang, X and Rabczuk, T},
	Doi = {10.1016/j.cma.2016.04.002},
	Issn = {00457825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Crack,Isogeometric analysis,NURBS,SGBEM,Weakly singular},
	Month = {jul},
	Pages = {252--275},
	Title = {{An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems}},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782516301402},
	Volume = {306},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782516301402},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.04.002}}

@article{Zechner2016212,
	Author = {J{\"u}rgen Zechner and Benjamin Marussig and Gernot Beer and Thomas-Peter Fries},
	Doi = {http://dx.doi.org/10.1016/j.cma.2016.03.043},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Collocation},
	Pages = {212 - 237},
	Title = {The isogeometric Nystr{\"o}m method},
	Url = {http://www.sciencedirect.com/science/article/pii/S004578251630130X},
	Volume = {308},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S004578251630130X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.03.043}}

@article{Simpson201287,
	Abstract = {The concept of isogeometric analysis, where functions that are used to describe geometry in \{CAD\} software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the \{NURBS\} approximation and \{BEM\} deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric \{BEM\} implementation. },
	Author = {R.N. Simpson and S.P.A. Bordas and J. Trevelyan and T. Rabczuk},
	Doi = {http://dx.doi.org/10.1016/j.cma.2011.08.008},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {NURBS},
	Pages = {87 - 100},
	Title = {A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782511002635},
	Volume = {209--212},
	Year = {2012},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782511002635},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2011.08.008}}

@article{Scott2013197,
	Abstract = {Abstract We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the B{\'e}zier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method. },
	Author = {M.A. Scott and R.N. Simpson and J.A. Evans and S. Lipton and S.P.A. Bordas and T.J.R. Hughes and T.W. Sederberg},
	Doi = {http://dx.doi.org/10.1016/j.cma.2012.11.001},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Collocation},
	Pages = {197 - 221},
	Title = {Isogeometric boundary element analysis using unstructured T-splines},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782512003386},
	Volume = {254},
	Year = {2013},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782512003386},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2012.11.001}}

@article{khajah2016isogeometric,
  title={Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems},
  author={Khajah, Tahsin and Antoine, Xavier and Bordas, St{\'e}phane},
  journal={arXiv preprint arXiv:1610.01694},
  year={2016}
}


@article{Simpson2014265,
	Abstract = {Abstract An isogeometric boundary element method based on T-splines is used to simulate acoustic phenomena. We restrict our developments to low-frequency problems to establish the fundamental properties of the proposed approach. Using T-splines, the computer aided design (CAD) and boundary element analysis are integrated without recourse to geometry clean-up or mesh generation. A regularized Burton--Miller formulation is used resulting in integrals which are at most weakly singular. We employ a collocation-based approach to generate the linear system of equations. The method is verified against closed-form solutions and direct comparisons are made with conventional Lagrangian discretizations. It is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the T-spline. The method is then applied to a real-world application to illustrate the potential for integrated engineering design and analysis. },
	Author = {R.N. Simpson and M.A. Scott and M. Taus and D.C. Thomas and H. Lian},
	Doi = {http://dx.doi.org/10.1016/j.cma.2013.10.026},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Burton--Miller},
	Pages = {265 - 290},
	Title = {Acoustic isogeometric boundary element analysis},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782513002788},
	Volume = {269},
	Year = {2014},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782513002788},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2013.10.026}}

@article{Marussig2015458,
	Abstract = {Abstract An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of \{NURBS\} basis functions is presented. The versatility and accuracy of the proposed methodology are demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions. },
	Author = {Benjamin Marussig and J{\"u}rgen Zechner and Gernot Beer and Thomas-Peter Fries},
	Doi = {http://dx.doi.org/10.1016/j.cma.2014.09.035},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Convergence},
	Note = {Isogeometric Analysis Special Issue},
	Pages = {458 - 488},
	Title = {Fast isogeometric boundary element method based on independent field approximation},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782514003582},
	Volume = {284},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782514003582},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2014.09.035}}

@article{Peake2015762,
	Abstract = {Abstract A boundary element method (BEM), based on non-uniform rational B-splines (NURBS), is used to find solutions to three-dimensional wave scattering problems governed by the Helmholtz equation. The method is extended in a partition-of-unity sense, multiplying the \{NURBS\} functions by families of plane waves; this method is called the eXtended Isogeometric Boundary Element Method (XIBEM). In this paper, the collocation \{XIBEM\} formulation is described and numerical results are given. The numerical results are compared against closed-form or converged solutions. Comparisons are made against the conventional boundary element method and the non-enriched isogeometric \{BEM\} (IGABEM). When compared to non-enriched boundary element simulations, using \{XIBEM\} significantly reduces the number of degrees of freedom required to obtain a solution of a given error; thus, with a fixed computational resource, problems of a shorter wavelength can be solved. },
	Author = {M.J. Peake and J. Trevelyan and G. Coates},
	Doi = {http://dx.doi.org/10.1016/j.cma.2014.10.039},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Partition of unity},
	Note = {Isogeometric Analysis Special Issue},
	Pages = {762 - 780},
	Title = {Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782514004095},
	Volume = {284},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782514004095},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2014.10.039}}

@article{Nguyen2016252,
	Abstract = {Abstract The isogeometric analysis is applied for the weakly singular symmetric Galerkin boundary element method (SGBEM) to analyze quasi-static elastic problems including crack problems in two-dimensional domains. This method takes the advantages from the common boundary representation of the isogeometric analysis and the boundary element method. The background of the developed method is to use non-uniform rational B-splines (NURBS) for the Galerkin approximation of both geometry and field variables (i.e. the displacement and traction on the boundary). The basic ingredient of the method is a pair of weakly-singular weak-form integral equations for the displacement and traction on the boundary. These integral equations contain at most weakly-singular kernels of ln r , where r is the distance from a source point to a field point. Various numerical examples are examined to validate the accuracy and efficiency of the proposed method. A model of crack propagation is also discussed to illustrate the use of the method for crack growth simulation. Through the numerical examples, it is observed that the isogeometric \{SGBEM\} produces highly accurate results yet it is simple to implement. },
	Author = {B.H. Nguyen and H.D. Tran and C. Anitescu and X. Zhuang and T. Rabczuk},
	Doi = {http://dx.doi.org/10.1016/j.cma.2016.04.002},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Weakly singular},
	Pages = {252 - 275},
	Title = {An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782516301402},
	Volume = {306},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782516301402},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.04.002}}

@article{Maestre2016112,
	Abstract = {Abstract In this paper we describe a three-dimensional Isogeometric Analysis based on the Boundary Element Method (IGA--BEM) in the time domain. We show the capabilities and accuracy of the method for the simulation of non-linear gravity waves. The flow is assumed to be inviscid and irrotational and this leads to a mixed boundary value problem governed by the Laplace's equation. The Boundary Integral Equation is solved at each time step and the time marching scheme is performed with a fourth-order Runge--Kutta method. The hydrodynamic force is calculated with an auxiliary boundary equation. In the simulations, the analysis suitable-T-spline and \{NURBS\} basis are used to approximate both the geometry and the \{BEM\} variables in the context of the B{\'e}zier extraction framework. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and \{NURBS\} basis, which makes the model numerically stable without the need of artificial smooth techniques; (2) the high geometrical approximation of the non-rational splines; (3) the refinement capabilities without affecting the geometry and \{BEM\} variables and (4) and the direct integration with computer aided geometrical design tools. Some numerical benchmark examples are analysed to demonstrate the accuracy and the stability of the method. In addition, we report simulations of waves generated by the movement of submerged foils, which have implications in some wave generator systems installed in surf parks. },
	Author = {Jorge Maestre and Ildefonso Cuesta and Jordi Pallares},
	Doi = {http://dx.doi.org/10.1016/j.cma.2016.06.031},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Surf park},
	Pages = {112 - 133},
	Title = {An unsteady 3D Isogeometrical Boundary Element Analysis applied to nonlinear gravity waves},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782516306569},
	Volume = {310},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782516306569},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.06.031}}

@article{Turco,
	Abstract = {The paper deals with the boundary element discretization of three-dimensional structural problems. A model, based on the management of the boundary
by macro-elements, the use of a B-spline quadratic description of the boundary variables and a systematic use of analytical integration,
is presented. By referring to rectangular piece-wise solids, the results of the analytical integration are given in a general form, utilizable for any order polynomial
shape functions. The discretization process has been designed with the aim of obtaining an accurate evaluation of the stress field. Two numerical tests, which can be compared with analytical and refined finite element solutions, have been selected to check the performance of the model.},
	Author = {Emilio Turco, Maurizio Aristodemo},
	Journal = {Appl. Mech. Engrg.},
	Pages = {119-128},
	Title = {A three-dimensional B-spline boundary element method},
	Volume = {155},
	Year = {1998}}

@article{Aimi2016,
	Abstract = {Abstract The application of the Isogeometric Analysis (IgA) paradigm to Symmetric Galerkin Boundary Element Method (SGBEM) is investigated. In order to obtain a very flexible approach, the study is here developed by using non-polynomial spline functions to represent both the domain boundary and the approximate solution. The numerical comparison between IGA-SGBEM and both curvilinear and standard \{SGBEM\} approaches shows the general capability of the presented method to produce accurate approximate solutions with less degrees of freedom. },
	Author = {A. Aimi and M. Diligenti and M.L. Sampoli and A. Sestini},
	Doi = {http://dx.doi.org/10.1016/j.apnum.2016.07.004},
	Issn = {0168-9274},
	Journal = {Applied Numerical Mathematics},
	Keywords = {Symmetric Galerkin boundary element method},
	Pages = {-},
	Title = {Non-polynomial spline alternatives in Isogeometric Symmetric Galerkin \{BEM\}},
	Url = {http://www.sciencedirect.com/science/article/pii/S0168927416301118},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0168927416301118},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.apnum.2016.07.004}}

@article{Feischl2016141,
	Abstract = {Abstract We derive and discuss a posteriori error estimators for Galerkin and collocation \{IGA\} boundary element methods for weakly singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error estimator for Galerkin \{IGA\} boundary element methods, the present work focuses more on collocation and weighted-residual error estimators, which provide reliable upper bounds for the energy error. Our analysis allows piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. We formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments show that the proposed adaptive strategy leads to optimal convergence, and related \{IGA\} boundary element methods are superior to standard boundary element methods with piecewise polynomials. },
	Author = {Michael Feischl and Gregor Gantner and Alexander Haberl and Dirk Praetorius},
	Doi = {http://dx.doi.org/10.1016/j.enganabound.2015.10.003},
	Issn = {0955-7997},
	Journal = {Engineering Analysis with Boundary Elements},
	Keywords = {Adaptive mesh-refinement},
	Pages = {141 - 153},
	Title = {Adaptive 2D \{IGA\} boundary element methods},
	Url = {http://www.sciencedirect.com/science/article/pii/S0955799715002155},
	Volume = {62},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0955799715002155},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.enganabound.2015.10.003}}

@article{GeneralizedIGABEMBeer2016,
	Abstract = {A novel approach to the simulation with the boundary element method using trimmed
NURBS patches is presented. The advantage of this approach is its efficiency and easy implementation.
The analysis with trimmed NURBS is achieved by double mapping. The variation of the unknowns on the
boundary is specified in a local coordinate system and is completely independent of the description of the
geometry. The method is tested on a branched tunnel and the results compared with those obtained from
a conventional analysis. The conclusion is that the proposed approach is superior in terms of number of
unknowns and effort required.},
	Author = {Gernot Beer and Benjamin Marussig and J{\"u}rgen Zechner and Christian D{\"u}nser and Thomas-Peter Fries},
	Title = {Boundary Element Analysis with trimmed NURBS and a generalized IGA approach},
	Url = {arXiv:1406.3499},
	Year = {2016},
	Bdsk-Url-1 = {arXiv:1406.3499}}

@article{TrimmedBeer2016,
	Author = {Benjamin Marussig and J{\"u}rgen Zechner and Gernot Beer and Thomas-Peter Fries},
	Title = {Stable Isogeometric Analysis of Trimmed Geometries},
	Url = {arXiv:1603.09660},
	Year = 2016,
	Bdsk-Url-1 = {arXiv:1603.09660}}

@article{ICESreport2015IGABEM,
	Abstract = {Isogeometric analysis is applied to boundary integral equations corresponding to boundary-value
problems governed by Laplace's equation. It is shown that the smoothness of geometric parametriza-
tions central to computer-aided design can be exploited for regularizing integral operators. As a result,
one obtains high-order collocation methods based on superior approximation and numerical integration
schemes and well-conditioned systems of linear algebraic equations. It is demonstrated that the proposed
approach allows one to solve boundary-value problems with an accuracy close to machine precision.},
	Author = {Matthias Taus, Gregory J. Rodin and Thomas J. R. Hughes},
	Journal = {ICES REPORT 15-12},
	Title = {Isogeometric Analysis of Boundary Integral Equations},
	Url = {https://www.ices.utexas.edu/media/reports/2015/1512.pdf},
	Year = 2015,
	Bdsk-Url-1 = {https://www.ices.utexas.edu/media/reports/2015/1512.pdf}}

@article{Soghrati201668,
	Abstract = {Abstract This manuscript introduces a NURBS-enhanced Hierarchical Interface-enriched Finite Element Method (NeHIFEM) for the mesh-independent treatment of multiphase problems with complex morphologies. The NeHIFEM implements a non-isoparametric mapping similar to that introduced in the \{NURBS\} Enhanced Finite Element Method (NEFEM) for the exact geometrical modeling of problems with curved materials interfaces. In this work, we propose a new generalized NURBS-enhanced mapping for triangular elements with three curvilinear edges, together with an isoparametric approach for evaluating basis functions in these elements to facilitate the construction of enrichment functions in the NeHIFEM. This unique capability allows the implementation of simple structured meshes for creating the computational model, while fully eliminating the geometric discretization error without introducing additional degrees of freedom. A new approach for the construction of higher-order enrichment functions in the NeHIFEM is also introduced to accurately capture gradient discontinuities along materials interfaces. Several example problems are presented to shed light on the accuracy and convergence rate of the NeHIFEM. We also show the application of this method for simulating the thermal and structural responses of heterogeneous materials with complex microstructures. },
	Author = {Soheil Soghrati and Ricardo Alvarez Merel},
	Doi = {http://dx.doi.org/10.1016/j.finel.2016.06.007},
	Issn = {0168-874X},
	Journal = {Finite Elements in Analysis and Design},
	Keywords = {Enrichment function},
	Pages = {68 - 79},
	Title = {\{NURBS\} enhanced HIFEM: A fully mesh-independent method with zero geometric discretization error},
	Url = {http://www.sciencedirect.com/science/article/pii/S0168874X16301007},
	Volume = {120},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0168874X16301007},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.finel.2016.06.007}}

@article{Antolin2015817,
	Abstract = {Abstract In this paper we discuss the use of the sum-factorization for the calculation of the integrals arising in Galerkin isogeometric analysis. While introducing very little change in an isogeometric code based on element-by-element quadrature and assembling, the sum-factorization approach, taking advantage of the tensor-product structure of splines or \{NURBS\} shape functions, significantly reduces the quadrature computational cost. },
	Author = {P. Antolin and A. Buffa and F. Calabr{\`o} and M. Martinelli and G. Sangalli},
	Doi = {http://dx.doi.org/10.1016/j.cma.2014.12.013},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Sum-factorization},
	Pages = {817 - 828},
	Title = {Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782514004927},
	Volume = {285},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782514004927},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2014.12.013}}

@article{Dalcin2016151,
	Abstract = {Abstract We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility of PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. We show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations. },
	Author = {L. Dalcin and N. Collier and P. Vignal and A.M.A. C{\^o}rtes and V.M. Calo},
	Doi = {http://dx.doi.org/10.1016/j.cma.2016.05.011},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Open-source software},
	Pages = {151 - 181},
	Title = {PetIGA: A framework for high-performance isogeometric analysis},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782516303401},
	Volume = {308},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782516303401},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.05.011}}

@article{Nguyen201589,
	Abstract = {Abstract Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. In this manuscript, through a self-contained Matlab{\textregistered} implementation, we present an introduction to \{IGA\} applied to simple analysis problems and the related computer implementation aspects. Furthermore, implementation of the extended \{IGA\} which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. We also describe the use of \{IGA\} in the context of strong-form (collocation) formulations, which has been an area of research interest due to the potential for significant efficiency gains offered by these methods. The code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The B{\'e}zier extraction concept that allows the \{FE\} analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA. },
	Author = {Vinh Phu Nguyen and Cosmin Anitescu and St{\'e}phane P.A. Bordas and Timon Rabczuk},
	Doi = {http://dx.doi.org/10.1016/j.matcom.2015.05.008},
	Issn = {0378-4754},
	Journal = {Mathematics and Computers in Simulation},
	Keywords = {Isogeometric collocation},
	Pages = {89 - 116},
	Title = {Isogeometric analysis: An overview and computer implementation aspects},
	Url = {http://www.sciencedirect.com/science/article/pii/S0378475415001214},
	Volume = {117},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0378475415001214},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.matcom.2015.05.008}}

@article{IGATOOLS,
	Abstract = {We present the design of an object oriented general purpose library for isogeometric analysis, where the mathematical concepts of the isogeometric method and their relationships are directly mapped into classes and their interactions. The encapsulation of mathematical concepts into interacting building blocks gives flexibility to use the library in a wide range of scientific areas and applications. We provide a precise framework for a lot of loose, available information regarding the implementation of the isogeometric method, and also discuss the similarities and differences between this and the finite element method. We also describe how to implement this proposed design in a C++11 open source library, \textttigatools (http://www.igatools.org). The library uses advanced object oriented and generic programming techniques to ensure reusability, reliability, and maintainability of the source code. It includes isogeometric elements of the h-div and h-curl type, and supports the development of dimension independent code (including manifolds and tensor-valued spaces). We finally present a number of code examples to illustrate the flexibility and power of the library, including surface domains, nonlinear elasticity, and Navier--Stokes computations on nontrivial geometries.},
	Author = {M. Sebastian Pauletti and Massimiliano Martinelli and Nicola Cavallini and and Pablo Antolin},
	Doi = {10.1137/140955252},
	Journal = {SIAM J. Sci. Comput., Software and High-Performance Computing},
	Title = {Igatools: An Isogeometric Analysis Library},
	Year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1137/140955252}}

@article{Reali,
	Abstract = { The concept of Isogeometric Analysis recently introduced by Hughes et al. [2005] is herein applied to the study of structural vibrations. In this framework, the favourable behaviour of the method is verified and compared with some classical finite element results. Numerical experiments are shown for structural one-, two- and three-dimensional problems in order to test the performance of this promising technique in the field of the analysis of natural frequencies and modes. },
	Author = {A. Reali},
	Doi = {10.1080/13632460609350626},
	Eprint = {http://dx.doi.org/10.1080/13632460609350626},
	Journal = {Journal of Earthquake Engineering},
	Number = {sup001},
	Pages = {1-30},
	Title = {AN ISO GEOMETRIC ANALYSIS APPROACH FOR THE STUDY OF STRUCTURAL VIBRATIONS},
	Url = {http://dx.doi.org/10.1080/13632460609350626},
	Volume = {10},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1080/13632460609350626}}

@article{GAMM:GAMM201410005,
	Author = {De Lorenzis, Laura and Wriggers, Peter and Hughes, Thomas J.R.},
	Doi = {10.1002/gamm.201410005},
	Issn = {1522-2608},
	Journal = {GAMM-Mitteilungen},
	Keywords = {contact mechanics, interface modeling, isogeometric analysis, NURBS, smoothing, state of the art review},
	Number = {1},
	Pages = {85--123},
	Publisher = {WILEY-VCH Verlag},
	Title = {Isogeometric contact: a review},
	Url = {http://dx.doi.org/10.1002/gamm.201410005},
	Volume = {37},
	Year = {2014},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/gamm.201410005}}

@article{Prieto1999247,
	Abstract = {A boundary element method (BEM) approach for the solution of the elastic problem with geometrical non-linearities is proposed. The geometrical non-linearities that are considered are both finite strains and large displacements. Material non-linearities are not considered in this paper, so the constitutive law employed is Hooke's elastic one and the fundamental solution introduced in the integral equations is the usual one for isotropic linear elasticity. In order to deal with the intricate non-linear equations that govern the problem, an incremental--iterative method is proposed. The equations are linearized and a Total Lagrangian Formulation is adopted. The integral equations of the \{BEM\} are developed in an incremental form. The iterative process is necessary in order to achieve a good approximation to the governing equations. The problem of a slab under homogeneous deformation is solved and the results obtained agree with the analytical solution. The problem of a hollow cylinder under internal pressure is also solved and its solution compared with that obtained by a standardized finite element method code. },
	Author = {I. Prieto and A.L. Ib{\'a}n and J.A. Garrido},
	Doi = {http://dx.doi.org/10.1016/S0955-7997(98)00079-4},
	Issn = {0955-7997},
	Journal = {Engineering Analysis with Boundary Elements},
	Keywords = {Field-boundary element method},
	Number = {3},
	Pages = {247 - 256},
	Title = {2D analysis for geometrically non-linear elastic problems using the \{BEM\}},
	Url = {http://www.sciencedirect.com/science/article/pii/S0955799798000794},
	Volume = {23},
	Year = {1999},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0955799798000794},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0955-7997(98)00079-4}}

@article{NOVATI1982136,
	Abstract = {The basic integral relationships for geometrically nonlinear problems are presented. Using the boundary element method they allow for the solution of a new range of problems in geometrically nonlinear elastostatics.},
	Author = {G Novati and C.A Brebbia},
	Doi = {http://dx.doi.org/10.1016/0307-904X(82)90025-7},
	Issn = {0307-904X},
	Journal = {Applied Mathematical Modelling},
	Keywords = {direct boundary integral equations},
	Number = {2},
	Pages = {136 - 138},
	Title = {Boundary element formulation for geometrically nonlinear elastostatics},
	Url = {http://www.sciencedirect.com/science/article/pii/0307904X82900257},
	Volume = {6},
	Year = {1982},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0307904X82900257},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/0307-904X(82)90025-7}}

@article{NME:NME1620360204,
	Author = {Karami, G.},
	Doi = {10.1002/nme.1620360204},
	Issn = {1097-0207},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {2},
	Pages = {221--235},
	Publisher = {John Wiley & Sons, Ltd},
	Title = {Boundary element analysis of two-dimensional elastoplastic contact problems},
	Url = {http://dx.doi.org/10.1002/nme.1620360204},
	Volume = {36},
	Year = {1993},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/nme.1620360204}}

@article{MARTIN1998349,
	Abstract = {A general boundary element formulation for contact problems, capable of dealing with local elastoplastic effects and friction, is presented. Both conforming and non-conforming problems may be analysed. The contact problem is solved by means of a direct constraint technique, in which compatibility and equilibrium conditions are directly enforced in the general system of equations. The contact areas are modelled with linear interpolation functions, and quadratic interpolation functions are used everywhere else. Elastoplasticity is solved by a BEM initial strain approach The Von Mises yield criterion with its associated flow rule is adopted. Both perfectly plastic and work hardening materials are studied in the proposed formulation. An incremental loading technique is proposed, which allows accurate development of the loading history of the problem. The non-linear nature of these problems demands the use of an iterative procedure, to determine the correct frictional conditions at every node of the contact area and the value of the plastic strains at selected points where local yielding may have occurred. Several numerical examples are presented to demonstrate the efficiency of the proposed formulation.},
	Author = {D Mart{\'\i}n and M.H Aliabadi},
	Doi = {http://dx.doi.org/10.1016/S0955-7997(98)00023-X},
	Issn = {0955-7997},
	Journal = {Engineering Analysis with Boundary Elements},
	Keywords = {friction},
	Number = {4},
	Pages = {349 - 360},
	Title = {Contact Mechanics Boundary element analysis of two-dimensional elastoplastic contact problems},
	Url = {http://www.sciencedirect.com/science/article/pii/S095579979800023X},
	Volume = {21},
	Year = {1998},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S095579979800023X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0955-7997(98)00023-X}}

@article{Kanber2003,
	Abstract = {An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.},
	Author = {Kanber, Bahattin and Guzelbey, Ibrahim H. and Erklig, Ahmet},
	Doi = {10.1007/BF02487812},
	Issn = {1614-3116},
	Journal = {Acta Mechanica Sinica},
	Number = {4},
	Pages = {347--354},
	Title = {Boundary element analysis of contact problems using artificial boundary node approach},
	Url = {http://dx.doi.org/10.1007/BF02487812},
	Volume = {19},
	Year = {2003},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02487812}}

@article{Ribeiro2008,
	Abstract = {Conventional numerical implementation of the boundary element method (BEM) for elasto-plastic analysis requires a domain discretization into cells. This requires more effort for the discretization of the problem and additional computational effort. A new technique is proposed here for the analysis of 2D and 3D elasto-plastic problems with the boundary element method. In this approach the domain does not need to be discretised into cells prior to the analysis. Plasticity is assumed to start from the boundary and the cells are generated from the boundary data automatically during the analysis. Using the cell generation process, elasto-plastic analysis with the BEM becomes much more user friendly and efficient than the standard approach with a pre-definition of cells. The accuracy and efficiency of the solution obtained by the new approach is verified by several numerical examples.},
	Author = {Ribeiro, T. S. A. and Beer, G. and Duenser, C.},
	Doi = {10.1007/s00466-007-0227-1},
	Issn = {1432-0924},
	Journal = {Computational Mechanics},
	Number = {5},
	Pages = {715--732},
	Title = {Efficient elastoplastic analysis with the boundary element method},
	Url = {http://dx.doi.org/10.1007/s00466-007-0227-1},
	Volume = {41},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00466-007-0227-1}}

@article{Aliabadi2,
	Abstract = {In this paper, elastoplastic contact problems with friction are solved by BEM, using non conforming discretisation. The contact conditions are directly enforced by relating tractions and displacements at every node of the contact zone with a point on the opposite surface. An ini- tial strain BEM formulation is used to study the elastoplastic problem. The material is assumed to obey the Von Mises yield criterion with its associated flow rule. A numerical application is presented, and the results are compared to those obtained by the use of conforming discretisation. Introduction The BEM is a powerful and efficient numerical technique for solving contact problems, as contact is inherent to the boundaries of the bodies involved. The application of BEM to a range of elastostatic, frictiona..},
	Author = {D. Martin and M.H. Aliabadi},
	Doi = {10.2495/BE970071},
	Pages = {9},
	Title = {Non-conforming BEM Discretisation In Frictional Elastoplastic Contact Problems},
	Volume = {19},
	Year = {1997},
	Bdsk-Url-1 = {http://dx.doi.org/10.2495/BE970071}}

@article{NME:NME1385,
	Author = {Bertoldi, Katia and Brun, Michele and Bigoni, Davide},
	Doi = {10.1002/nme.1385},
	Issn = {1097-0207},
	Journal = {International Journal for Numerical Methods in Engineering},
	Keywords = {Green's function, boundary integral equations, boundary elements, elastoplasticity, domain integrals},
	Number = {7},
	Pages = {877--906},
	Publisher = {John Wiley & Sons, Ltd.},
	Title = {A new boundary element technique without domain integrals for elastoplastic solids},
	Url = {http://dx.doi.org/10.1002/nme.1385},
	Volume = {64},
	Year = {2005},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/nme.1385}}

@article{HyperElasticBEM,
	Abstract = { This paper develops the necessary derivations for the boundary element method as applied to elastomers and presents a comparison between analytical and numerical solutions to the standard patch test using the Mooney-Rivlin strain energy formulation. The case of a pressurised thick walled cylinder is also examined to test for symmetry of the displacement solution.},
	Author = {M. Bayliss & A. El-Zafrany},
	Doi = {10.2495/BE020311},
	Pages = {12},
	Title = {Boundary Element Analysis Of Hyper-elastic Elastomeric Materials},
	Volume = {32},
	Year = {2002},
	Bdsk-Url-1 = {http://dx.doi.org/10.2495/BE020311}}

@article{Wei2016,
	Abstract = {Abstract In this paper, we present Truncated T-splines as a new type of T-splines suitable for both geometric design and analysis, supporting highly localized refinement. Truncated T-spline basis functions are piece-wise polynomials that are linearly independent and form a partition of unity. Refinement of truncated T-splines produces nested spline spaces. Furthermore, we study truncated T-splines and local refinement on the general domain (2-manifold) with extraordinary points in the T-mesh. G 1 continuity is attained around extraordinary points by properly capping quartic B{\'e}zier patches, where a constrained optimization problem is solved. In the end, we study benchmark problems using truncated T-splines in the context of isogeometric analysis. We also apply truncated T-splines to complex geometries to show the smooth surfaces and simulation results under local refinement. },
	Author = {Xiaodong Wei and Yongjie Zhang and Lei Liu and Thomas J.R. Hughes},
	Doi = {http://dx.doi.org/10.1016/j.cma.2016.07.020},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Isogeometric analysis},
	Pages = {-},
	Title = {Truncated T-splines: Fundamentals and methods},
	Url = {http://www.sciencedirect.com/science/article/pii/S004578251630771X},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S004578251630771X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.07.020}}

@article{Ghorashi2015138,
	Abstract = {Abstract Fracture analysis of orthotropic cracked media is investigated by applying the recently developed extended isogeometric analysis (XIGA) (Ghorashi et al., 2012) using the T-spline basis functions. The signed distance function and orthotropic crack tip enrichment functions are adopted for extrinsically enriching the conventional isogeometric analysis approximation for representation of strong discontinuity and reproducing the stress singular field around a crack tip, respectively. Moreover, by applying the T-spline basis functions, \{XIGA\} is further developed to make the local refinement feasible. For increasing the integration accuracy, the 'sub-triangle' and 'almost polar' techniques are adopted for the cut and crack tip elements, respectively. The interaction integral technique developed by Kim and Paulino (2003) is applied for computing the mixed mode stress intensity factors (SIFs). Finally, the proposed approach is applied for analysis of some cracked orthotropic problems and the mixed mode \{SIFs\} are compared with those of other methods available in the literature. },
	Author = {S.Sh. Ghorashi and N. Valizadeh and S. Mohammadi and T. Rabczuk},
	Doi = {http://dx.doi.org/10.1016/j.compstruc.2014.09.017},
	Issn = {0045-7949},
	Journal = {Computers & Structures},
	Keywords = {Local refinement},
	Note = {CIVIL-COMP},
	Pages = {138 - 146},
	Title = {T-spline based \{XIGA\} for fracture analysis of orthotropic media},
	Url = {http://www.sciencedirect.com/science/article/pii/S004579491400217X},
	Volume = {147},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S004579491400217X},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.compstruc.2014.09.017}}

@article{Evans20151,
	Abstract = {Abstract In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of T-spline spaces results in simple, highly localized refinement algorithms which can be utilized in a design or analysis context. A detailed theoretical formulation is presented. B{\'e}zier extraction is extended to \{HASTS\} simplifying the implementation of \{HASTS\} in existing finite element codes. The behavior of a simple \{HASTS\} refinement algorithm is compared to the local refinement algorithm for analysis-suitable T-splines demonstrating the superior efficiency and locality of the \{HASTS\} algorithm. Finally, \{HASTS\} are utilized as a basis for adaptive isogeometric analysis. },
	Author = {E.J. Evans and M.A. Scott and X. Li and D.C. Thomas},
	Doi = {http://dx.doi.org/10.1016/j.cma.2014.05.019},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {T-splines},
	Note = {Isogeometric Analysis Special Issue},
	Pages = {1 - 20},
	Title = {Hierarchical T-splines: Analysis-suitability, B{\'e}zier extraction, and application as an adaptive basis for isogeometric analysis},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782514001807},
	Volume = {284},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782514001807},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2014.05.019}}

@article{Chavan20074075,
	Abstract = {The uniform convergence of finite element approximations based on a modified Hu--Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases that are well known, as well as newly constructed bases. Starting from a suitable three-field problem, we extend our α-dependent three-field formulation to geometrically nonlinear elasticity with Saint-Venant Kirchhoff law. Additionally, an α-dependent three-field formulation for a general hyperelastic material model is proposed. A range of numerical examples using different material laws for small and large strain elasticity is presented. },
	Author = {K.S. Chavan and B.P. Lamichhane and B.I. Wohlmuth},
	Doi = {http://dx.doi.org/10.1016/j.cma.2007.03.022},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Uniform convergence},
	Number = {41--44},
	Pages = {4075 - 4086},
	Title = {Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782507001806},
	Volume = {196},
	Year = {2007},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782507001806},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2007.03.022}}

@article{Kruse201573,
	Abstract = {Abstract Isogeometric collocation methods have been recently proposed as an alternative to standard Galerkin approaches as they provide a significant reduction in computational cost for higher-order discretizations. In this work, we explore the application of isogeometric collocation to large deformation elasticity and frictional contact problems. We first derive the non-linear governing equations for the elasticity problem with finite deformation kinematics and provide details on their consistent linearization. Some numerical examples demonstrate the performance of collocation in its basic and enhanced versions, differing by the enforcement of Neumann boundary conditions. For problems with strong singularities, enhanced collocation is shown to outperform basic collocation and to lead to a spatial convergence behavior very similar to Galerkin, whereas for weaker or no singularities enhanced and basic collocation may give very similar results. A large deformation contact formulation is subsequently developed and tested in the frictional setting, where collocation confirms the excellent performance already obtained for the frictionless case. Finally, it is shown that the contact formulation in the collocation framework passes the contact patch test to machine precision in a three-dimensional setting with arbitrarily inclined non-matching discretizations, thus outperforming most of the available contact formulations and all those with pointwise enforcement of the contact constraints. },
	Author = {R. Kruse and N. Nguyen-Thanh and L. De Lorenzis and T.J.R. Hughes},
	Doi = {http://dx.doi.org/10.1016/j.cma.2015.07.022},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Frictional contact},
	Pages = {73 - 112},
	Title = {Isogeometric collocation for large deformation elasticity and frictional contact problems},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782515002406},
	Volume = {296},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782515002406},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2015.07.022}}

@article{Brun20032461,
	Abstract = {Incremental elastic deformations superimposed upon a given homogeneous strain are analyzed with a boundary element technique. This is based on a recently-developed Green's function for non-linear incremental elastic deformations. Plane strain perturbations are considered of a broad class of incompressible material behaviours (including hyper-, hypoelastic and Navier--Stokes constitutive equations) within the elliptic range. Numerical treatment of the problem is detailed. A possibility of employing the method in the fully non-linear range is outlined, which yields a boundary element approach where the use of domain integrals is avoided, at least in a conventional sense. The methods for bifurcation and shear band analyses will be reported in Part II. },
	Author = {M. Brun and D. Capuani and D. Bigoni},
	Doi = {http://dx.doi.org/10.1016/S0045-7825(03)00268-8},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Number = {22--24},
	Pages = {2461 - 2479},
	Title = {A boundary element technique for incremental, non-linear elasticity: Part I: Formulation},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782503002688},
	Volume = {192},
	Year = {2003},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782503002688},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0045-7825(03)00268-8}}

@article{Bigoni2002471,
	Abstract = {An elastic, incompressible, infinite body is considered subject to plane and homogeneous deformation. At a certain value of the loading, when the material is still in the elliptic range, an incremental concentrated line load is considered acting at an arbitrary location in the body and extending orthogonally to the plane of deformation. This plane strain problem is solved, so that a Green's function for incremental, nonlinear elastic deformation is obtained. This is used in two different ways: to quantify the decay rate of self-equilibrated loads in a homogeneously stretched elastic solid; and to give a boundary element formulation for incremental deformations superimposed upon a given homogeneous strain. The former result provides a perturbative approach to shear bands, which are shown to develop in the elliptic range, induced by self-equilibrated perturbations. The latter result lays the foundations for a rigorous approach to boundary element techniques in finite strain elasticity. },
	Author = {Davide Bigoni and Domenico Capuani},
	Doi = {http://dx.doi.org/10.1016/S0022-5096(01)00090-4},
	Issn = {0022-5096},
	Journal = {Journal of the Mechanics and Physics of Solids},
	Keywords = {Boundary element method},
	Number = {3},
	Pages = {471 - 500},
	Title = {Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation},
	Url = {http://www.sciencedirect.com/science/article/pii/S0022509601000904},
	Volume = {50},
	Year = {2002},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0022509601000904},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0022-5096(01)00090-4}}

@article{GeomNonLinearBEM,
	Author = {Shiue, Fuh-Cwo},
	Journal = {Retrospective Theses and Dissertations. Paper 9082.},
	Title = {Geometrically nonlinear analysis for an elastic body by the boundary element method},
	Url = {http://lib.dr.iastate.edu/rtd/9082},
	Year = {1989},
	Bdsk-Url-1 = {http://lib.dr.iastate.edu/rtd/9082}}

@article{NME:NME2765,
	Author = {Panzeca, T. and Terravecchia, S. and Zito, L.},
	Doi = {10.1002/nme.2765},
	Issn = {1097-0207},
	Journal = {International Journal for Numerical Methods in Engineering},
	Keywords = {inelastic action, symmetric BEM, singular domain integral, Radial Integral Method},
	Number = {2},
	Pages = {184--204},
	Publisher = {John Wiley & Sons, Ltd.},
	Title = {Computational aspects in 2D SBEM analysis with domain inelastic actions},
	Url = {http://dx.doi.org/10.1002/nme.2765},
	Volume = {82},
	Year = {2010},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/nme.2765}}

@article{colli2009boundary,
	Author = {Colli, Sergia and Gei, Massimiliano and Bigoni, Davide},
	Journal = {Computer Modeling in Engineering and Sciences (CMES)},
	Number = {1},
	Pages = {29},
	Title = {A boundary element formulation for incremental nonlinear elastic deformation of compressible solids},
	Volume = {40},
	Year = {2009}}

@article{Hughes20054135,
	Author = {T.J.R. Hughes and J.A. Cottrell and Y. Bazilevs},
	Doi = {http://dx.doi.org/10.1016/j.cma.2004.10.008},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {k-refinement},
	Number = {39--41},
	Pages = {4135 - 4195},
	Title = {Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782504005171},
	Volume = {194},
	Year = {2005},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782504005171},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2004.10.008}}

@article{Peng3D,
	Abstract = {Abstract We present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). \{NURBS\} basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the \{CAD\} model of the component under consideration. },
	Author = {X. Peng and E. Atroshchenko and P. Kerfriden and S.P.A. Bordas},
	Doi = {http://dx.doi.org/10.1016/j.cma.2016.05.038},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Fracture simulations directly from \{CAD\}},
	Pages = {-},
	Title = {Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782516304832},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782516304832},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2016.05.038}}

@article{Peng2D,
	Author = {X. Peng and E. Atroshchenko and P. Kerfriden and S.P.A. Bordas},
	Journal = {International Journal of Fracture},
	Title = {Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment},
	Year = {2016 (accepted for publication)}}

@article{Bordas2008943,
	Author = {Bordas, S. and Rabczuk, T. and Zi, G.},
	Document_Type = {Article},
	Doi = {10.1016/j.engfracmech.2007.05.010},
	Journal = {Engineering Fracture Mechanics},
	Note = {cited By 164},
	Number = {5},
	Pages = {943-960},
	Source = {Scopus},
	Title = {Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment},
	Url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-36849039473&partnerID=40&md5=e929fdba477e8e6e4d6154d1469e06a2},
	Volume = {75},
	Year = {2008},
	Bdsk-Url-1 = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-36849039473&partnerID=40&md5=e929fdba477e8e6e4d6154d1469e06a2},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.engfracmech.2007.05.010}}

@article{Chen1988,
	Author = {Hong, H.K. and Chen, J.T.},
	Journal = {Journal of Engineering Mechanics},
	Number = {6},
	Pages = {1028-1044},
	Title = {Derivations of integral equations of elasticity},
	Volume = {114},
	Year = {1988}}

@article{NME:NME1620330611,
	Author = {Portela, A. and Aliabadi, M. H. and Rooke, D. P.},
	Doi = {10.1002/nme.1620330611},
	Issn = {1097-0207},
	Journal = {International Journal for Numerical Methods in Engineering},
	Number = {6},
	Pages = {1269--1287},
	Publisher = {John Wiley & Sons, Ltd},
	Title = {The dual boundary element method: Effective implementation for crack problems},
	Url = {http://dx.doi.org/10.1002/nme.1620330611},
	Volume = {33},
	Year = {1992},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/nme.1620330611}}

@article{MI1992161,
	Abstract = {In this paper, an effective numerical implementation of the three-dimensional dual boundary element method, for linear elastic crack problems, is presented. Displacement and traction integral equations which constitute the dual boundary formulation are used independently on crack surfaces to overcome the numerical difficulties associated with co-planar crack surfaces in boundary element analysis. The crack surfaces are modelled with discontinous quadrilateral quadratic elements. The use of discontinous elements allow for accurate integration of finite part integrals. The accuracy of the proposed method is demonstrated by solving a number of problems including edge and embedded cracks.},
	Author = {Y. Mi and M.H. Aliabadi},
	Doi = {http://dx.doi.org/10.1016/0955-7997(92)90047-B},
	Issn = {0955-7997},
	Journal = {Engineering Analysis with Boundary Elements},
	Number = {2},
	Pages = {161 - 171},
	Title = {Dual boundary element method for three-dimensional fracture mechanics analysis},
	Url = {http://www.sciencedirect.com/science/article/pii/095579979290047B},
	Volume = {10},
	Year = {1992},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/095579979290047B},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/0955-7997(92)90047-B}}

@book{NURBSbook,
	Author = {Piegl, Les and Tiller, Wayne},
	Publisher = {Springer},
	Title = {The NURBS book},
	Year = {1997}}

@book{cottrell2009isogeometric,
	Author = {Cottrell, J Austin and Hughes, Thomas JR and Bazilevs, Yuri},
	Publisher = {John Wiley \& Sons},
	Title = {Isogeometric analysis: toward integration of CAD and FEA},
	Year = {2009}}

@article{Cisilino20041157,
	Abstract = {In this paper a general procedure for the analysis of three-dimensional multiple fatigue crack growth is presented. The crack propagation is simulated using an incremental crack extension analysis based on the strain energy density criterion and the Paris law. For each crack extension the dual boundary element method is used to perform single region analysis of the cracked component. Stress intensity factors are computed along the crack fronts using a displacement-based method. Crack extensions are automatically modelled with the introduction of new boundary elements along the crack fronts and a localized rediscretization in the area where the cracks intersect the free surfaces. The capability of the procedure is demonstrated by solving a number of multiple edge-crack examples. Results are compared with experimental observations. },
	Author = {Adri{\'a}n P. Cisilino and M.H. Aliabadi},
	Doi = {http://dx.doi.org/10.1016/j.enganabound.2004.01.005},
	Issn = {0955-7997},
	Journal = {Engineering Analysis with Boundary Elements},
	Keywords = {Dual Boundary Element Method},
	Number = {9},
	Pages = {1157 - 1173},
	Title = {Dual boundary element assessment of three-dimensional fatigue crack growth},
	Url = {http://www.sciencedirect.com/science/article/pii/S0955799704000232},
	Volume = {28},
	Year = {2004},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0955799704000232},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.enganabound.2004.01.005}}

@article{NguyenThanh20111892,
	Abstract = {Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method. },
	Author = {N. Nguyen-Thanh and H. Nguyen-Xuan and S.P.A. Bordas and T. Rabczuk},
	Doi = {http://dx.doi.org/10.1016/j.cma.2011.01.018},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {PHT-spline},
	Number = {21--22},
	Pages = {1892 - 1908},
	Title = {Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782511000338},
	Volume = {200},
	Year = {2011},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782511000338},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2011.01.018}}

@article{Vuong20113554,
	Abstract = {Adaptive local refinement is one of the key issues in isogeometric analysis. In this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical B-splines. We investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity. Furthermore, we use concepts well-established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting. This also allows us to access a posteriori error estimation techniques. Numerical results for several different examples are given and they turn out to be very promising. },
	Author = {A.-V. Vuong and C. Giannelli and B. J{\"u}ttler and B. Simeon},
	Doi = {http://dx.doi.org/10.1016/j.cma.2011.09.004},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {Local refinement},
	Number = {49--52},
	Pages = {3554 - 3567},
	Title = {A hierarchical approach to adaptive local refinement in isogeometric analysis},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782511002933},
	Volume = {200},
	Year = {2011},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782511002933},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2011.09.004}}

@article{Deng200876,
	Abstract = {In this paper, we introduce a new type of splines---polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed construction process of spline basis functions over T-meshes which have the same important properties as B-splines do, such as nonnegativity, local support and partition of unity. As two fundamental operations, cross insertion and cross removal of PHT-splines are discussed. With the new splines, surface models can be constructed efficiently and adaptively to fit open or closed mesh models, where only linear systems of equations with a few unknowns are involved. With this approach, a \{NURBS\} surface can be efficiently simplified into a PHT-spline which dramatically reduces the superfluous control points of the \{NURBS\} surface. Furthermore, PHT-splines allow for several important types of geometry processing in a natural and efficient manner, such as conversion of a PHT-spline into an assembly of tensor-product spline patches, and shape simplification of PHT-splines over a coarser T-mesh. PHT-splines not only inherit many good properties of Sederberg's T-splines such as adaptivity and locality, but also extend T-splines in several aspects except that they are only C 1 continuous. For example, PHT-splines are polynomial instead of rational; cross insertion/removal of PHT-splines is local and simple. },
	Author = {Jiansong Deng and Falai Chen and Xin Li and Changqi Hu and Weihua Tong and Zhouwang Yang and Yuyu Feng},
	Doi = {http://dx.doi.org/10.1016/j.gmod.2008.03.001},
	Issn = {1524-0703},
	Journal = {Graphical Models},
	Keywords = {Shape simplification},
	Number = {4},
	Pages = {76 - 86},
	Title = {Polynomial splines over hierarchical T-meshes},
	Url = {http://www.sciencedirect.com/science/article/pii/S1524070308000039},
	Volume = {70},
	Year = {2008},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1524070308000039},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.gmod.2008.03.001}}

@article{Li2016,
	Abstract = {This paper provides a survey of local refinable splines, including hierarchical B-splines, T-splines, polynomial splines over T-meshes, etc., with a view to applications in geometric modeling and iso-geometric analysis. We will identify the strengths and weaknesses of these methods and also offer suggestions for their using in geometric modeling and iso-geometric analysis.},
	Author = {Li, Xin and Chen, FaLai and Kang, HongMei and Deng, JianSong},
	Doi = {10.1007/s11425-015-5063-8},
	Issn = {1869-1862},
	Journal = {Science China Mathematics},
	Number = {4},
	Pages = {617--644},
	Title = {A survey on the local refinable splines},
	Url = {http://dx.doi.org/10.1007/s11425-015-5063-8},
	Volume = {59},
	Year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11425-015-5063-8}}

@article{Wang20111438,
	Abstract = {Polynomial splines over hierarchical T-meshes (PHT-splines) have an efficient and simple local refinement algorithm, but fail to represent exactly certain complex engineering geometries. In this paper, based on the current isogeometric framework, we overcome the drawbacks of PHT-splines by extending these to Rational PHT-splines (RPHT-splines), and explore RPHT-splines as the basis for analysis. A residual-based posteriori error estimator using RPHT-splines basis functions is derived to guide the local refinement process adaptively. Numerical examples show the potential of RPHT-splines as the basis for the adaptive isogeometric analysis. },
	Author = {Ping Wang and Jinlan Xu and Jiansong Deng and Falai Chen},
	Doi = {http://dx.doi.org/10.1016/j.cad.2011.08.026},
	Issn = {0010-4485},
	Journal = {Computer-Aided Design},
	Keywords = {Residual-based a posteriori error estimator},
	Note = {Solid and Physical Modeling 2011},
	Number = {11},
	Pages = {1438 - 1448},
	Title = {Adaptive isogeometric analysis using rational PHT-splines},
	Url = {http://www.sciencedirect.com/science/article/pii/S0010448511002259},
	Volume = {43},
	Year = {2011},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0010448511002259},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cad.2011.08.026}}

@article{Rypl2012116,
	Abstract = {During the last decades, the finite element method has become the most powerful tool for structural analysis massively used in practical engineering. However, recently the isogeometric analysis has been introduced as a viable alternative to the standard, polynomial-based finite element analysis. Moreover, it has been shown that it may outperform the classical finite element method in many aspects. This paper presents how the isogeometric analysis can be integrated within an object oriented finite element environment. The class hierarchy and corresponding methods are designed in such a way, that most of the existing functionality of the finite element code is reused. The missing data and algorithms are developed and implemented in such a way that the object oriented features, such as modularity, extensibility, maintainability, and robustness, are fully retained. The performance of the implemented isogeometric analysis methodology is presented on two- and three-dimensional examples. },
	Author = {Daniel Rypl and Bo{\v r}ek Patz{\'a}k},
	Doi = {http://dx.doi.org/10.1016/j.advengsoft.2011.05.032},
	Issn = {0965-9978},
	Journal = {Advances in Engineering Software},
	Keywords = {Finite element method},
	Note = {CIVIL-COMP},
	Number = {1},
	Pages = {116 - 125},
	Title = {From the finite element analysis to the isogeometric analysis in an object oriented computing environment},
	Url = {http://www.sciencedirect.com/science/article/pii/S0965997811001529},
	Volume = {44},
	Year = {2012},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0965997811001529},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.advengsoft.2011.05.032}}

@article{deFalcoRV-11-GeoPDE,
	Author = {C. de Falco and A. Reali and R. Vazquez},
	Doi = {http://dx.doi.org/10.1016/j.advengsoft.2011.05.032},
	Journal = {Advances in Engineering Software},
	Number = {12},
	Pages = {1020 - 1034},
	Title = {GeoPDEs: a research tool for Isogeometric Analysis of PDEs},
	Volume = {42},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.advengsoft.2011.05.032}}

@article{Vazquez-16-GeoPDE,
	Author = {R. Vazquez},
	Doi = {http://dx.doi.org/10.1016/j.camwa.2016.05.010},
	Journal = {Computer \& Methods with Applications},
	Number = {3},
	Pages = {523 - 554},
	Title = {A new design for the implementation of isogeometric analysis in Octave and Matlab: GeoPDEs 3.0},
	Volume = {72},
	Year = {2016},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.camwa.2016.05.010}}

@article{NME:NME292,
	Author = {Kagan, Pavel and Fischer, Anath and Bar-Yoseph, Pinhas Z.},
	Doi = {10.1002/(SICI)1097-0207(19980215)41:3<435::AID-NME292>3.0.CO;2-U},
	Issn = {1097-0207},
	Journal = {International Journal for Numerical Methods in Engineering},
	Keywords = {geometrical design, physically based system, B-spline, finite element},
	Number = {3},
	Pages = {435--458},
	Publisher = {John Wiley & Sons, Ltd},
	Title = {New B-Spline Finite Element approach for geometrical design and mechanical analysis},
	Url = {http://dx.doi.org/10.1002/(SICI)1097-0207(19980215)41:3<435::AID-NME292>3.0.CO;2-U},
	Volume = {41},
	Year = {1998},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/(SICI)1097-0207(19980215)41:3%3C435::AID-NME292%3E3.0.CO;2-U}}

@article{BeiraodaVeiga2011,
	Abstract = {In this paper, we propose a theoretical study of the approximation properties of NURBS spaces, which are used in Isogeometric Analysis. We obtain error estimates that are explicit in terms of the mesh-size h, the degree p and the global regularity, measured by the parameter k. Our approach covers the approximation with global regularity from C                        0 up to C                        k--1, with 2k − 1 ≤ p. Notice that the interesting case of higher regularity, up to k = p, is still open. However, our results give an indication of the role of the smoothness k in the approximation properties, and offer a first mathematical justification of the potential of Isogeometric Analysis based on globally smooth NURBS.},
	Author = {Beir{\~a}o da Veiga, L. and Buffa, A. and Rivas, J. and Sangalli, G.},
	Doi = {10.1007/s00211-010-0338-z},
	Issn = {0945-3245},
	Journal = {Numerische Mathematik},
	Number = {2},
	Pages = {271--305},
	Title = {Some estimates for h--p--k-refinement in Isogeometric Analysis},
	Url = {http://dx.doi.org/10.1007/s00211-010-0338-z},
	Volume = {118},
	Year = {2011},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00211-010-0338-z}}

@article{HughesErrorIGA,
	Author = {Bazilevs, Y. and Beirao Da Veiga, L. and Cottrell, J. A. and Hughes, T. J. R. and Sangalli, G.},
	Doi = {10.1142/S0218202506001455},
	Eprint = {http://www.worldscientific.com/doi/pdf/10.1142/S0218202506001455},
	Journal = {Mathematical Models and Methods in Applied Sciences},
	Number = {07},
	Pages = {1031-1090},
	Title = {Isogeometric analysis: approximation, stability and error estimates for \emph{h}-refined meshes},
	Url = {http://www.worldscientific.com/doi/abs/10.1142/S0218202506001455},
	Volume = {16},
	Year = {2006},
	Bdsk-Url-1 = {http://www.worldscientific.com/doi/abs/10.1142/S0218202506001455},
	Bdsk-Url-2 = {http://dx.doi.org/10.1142/S0218202506001455}}

@article{Bazilevs2008,
	Abstract = {We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian--Eulerian description is utilized for the fluid subdomain and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations; the conservation properties of the semi-discrete and fully discretized systems; a unified presentation of the generalized-$\alpha$ time integration method for fluid-structure interaction; and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization and three numerical examples are presented which demonstrate the good behavior of the methodology.},
	Author = {Bazilevs, Y. and Calo, V. M. and Hughes, T. J. R. and Zhang, Y.},
	Doi = {10.1007/s00466-008-0315-x},
	Issn = {1432-0924},
	Journal = {Computational Mechanics},
	Number = {1},
	Pages = {3--37},
	Title = {Isogeometric fluid-structure interaction: theory, algorithms, and computations},
	Url = {http://dx.doi.org/10.1007/s00466-008-0315-x},
	Volume = {43},
	Year = {2008},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00466-008-0315-x}}

@article{Benson2010276,
	Abstract = {A Reissner--Mindlin shell formulation based on a degenerated solid is implemented for NURBS-based isogeometric analysis. The performance of the approach is examined on a set of linear elastic and nonlinear elasto-plastic benchmark examples. The analyses were performed with LS-DYNA, an industrial, general-purpose finite element code, for which a user-defined shell element capability was implemented. This new feature, to be reported on in subsequent work, allows for the use of \{NURBS\} and other non-standard discretizations in a sophisticated nonlinear analysis framework. },
	Author = {D.J. Benson and Y. Bazilevs and M.C. Hsu and T.J.R. Hughes},
	Doi = {http://dx.doi.org/10.1016/j.cma.2009.05.011},
	Issn = {0045-7825},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Keywords = {User-defined elements},
	Note = {Computational Geometry and Analysis},
	Number = {5--8},
	Pages = {276 - 289},
	Title = {Isogeometric shell analysis: The Reissner--Mindlin shell},
	Url = {http://www.sciencedirect.com/science/article/pii/S0045782509001820},
	Volume = {199},
	Year = {2010},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0045782509001820},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cma.2009.05.011}}

@article{Aimi2016173,
	Abstract = {Abstract Isogeometric approach applied to Boundary Element Methods is an emerging research area (see e.g. Simpson et al. (2012) [33]). In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element Method (SGBEM) devoted to the solution of 2D boundary value problems for the Laplace equation, where the boundary and the unknowns on it are both represented by B-splines (de Boor (2001) [9]). We mainly compare this approach, which we call IGA-SGBEM, with a curvilinear \{SGBEM\} (Aimi et al. (1999) [2]), which operates on any boundary given by explicit parametric representation and where the approximate solution is obtained using Lagrangian basis. Both techniques are further compared with a standard (conventional) \{SGBEM\} approach (Aimi et al. (1997) [1]), where the boundary of the assigned problem is approximated by linear elements and the numerical solution is expressed in terms of Lagrangian basis. Several examples will be presented and discussed, underlying benefits and drawbacks of all the above-mentioned approaches. },
	Author = {A. Aimi and M. Diligenti and M.L. Sampoli and A. Sestini},
	Doi = {http://dx.doi.org/10.1016/j.amc.2015.08.097},
	Issn = {0096-3003},
	Journal = {Applied Mathematics and Computation},
	Keywords = {Symmetric Galerkin Boundary Element Method},
	Note = {Subdivision, Geometric and Algebraic Methods, Isogeometric Analysis and Refinability},
	Pages = {173 - 186},
	Title = {Isogemetric analysis and symmetric Galerkin BEM: A 2D numerical study},
	Url = {http://www.sciencedirect.com/science/article/pii/S0096300315011534},
	Volume = {272, Part 1},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0096300315011534},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.amc.2015.08.097}}

@article{Sirtori1992255,
	Author = {Sirtori, S. and Maier, G. and Novati, G. and Miccoli, S.},
	Document_Type = {Article},
	Journal = {International Journal for Numerical Methods in Engineering},
	Note = {cited By 125},
	Number = {2},
	Pages = {255-282},
	Source = {Scopus},
	Title = {Galerkin symmetric boundary-element method in elasticity: Formulation and implementation},
	Url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0026905548&partnerID=40&md5=639c12023091eef128ce3ea873f34197},
	Volume = {35},
	Year = {1992},
	Bdsk-Url-1 = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-0026905548&partnerID=40&md5=639c12023091eef128ce3ea873f34197}}

@article{SederbergCFNZL-04-TSplines,
	Acmid = {1015715},
	Address = {New York, NY, USA},
	Author = {Sederberg, T.W. and Cardon, D.L. and Finnigan, G.T. and North, N.S. and Zheng, J. and Lyche, T.},
	Doi = {10.1145/1015706.1015715},
	Issn = {0730-0301},
	Issue_Date = {August 2004},
	Journal = {ACM Trans. Graph.},
	Keywords = {NURBS surfaces, T-splines, knot removal, local refinement, subdivision surfaces},
	Month = aug,
	Number = {3},
	Numpages = {8},
	Pages = {276--283},
	Publisher = {ACM},
	Title = {T-spline Simplification and Local Refinement},
	Url = {http://doi.acm.org/10.1145/1015706.1015715},
	Volume = {23},
	Year = {2004},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/1015706.1015715},
	Bdsk-Url-2 = {http://dx.doi.org/10.1145/1015706.1015715}}

@article{SederbergZBN-03-TSplines,
	Acmid = {1015715},
	Address = {New York, NY, USA},
	Author = {Sederberg, T.W. and Zheng, J. and Bakenov, A. and Nasri, A.},
	Doi = {10.1145/882262.882295},
	Issn = {0730-0301},
	Issue_Date = {August 2003},
	Journal = {ACM Trans. Graph.},
	Keywords = {NURBS surfaces, T-splines, knot removal, local refinement, subdivision surfaces},
	Month = aug,
	Number = {3},
	Numpages = {8},
	Pages = {477--484},
	Publisher = {ACM},
	Title = {T-splines and {T-NURCCs}},
	Url = {http://doi.acm.org/10.1145/1015706.1015715},
	Volume = {22},
	Year = {2003},
	Bdsk-Url-1 = {http://doi.acm.org/10.1145/1015706.1015715},
	Bdsk-Url-2 = {http://dx.doi.org/10.1145/882262.882295}}

@article{da2011isogeometric,
	Author = {da Veiga, L Beirao and Buffa, A and Cho, D and Sangalli, G},
	Journal = {Computer methods in applied mechanics and engineering},
	Number = {21},
	Pages = {1787--1803},
	Publisher = {North-Holland},
	Title = {IsoGeometric analysis using T-splines on two-patch geometries},
	Volume = {200},
	Year = {2011}}

@article{beirao2013analysis,
	Author = {Beir{\~a}o da Veiga, L and Buffa, A and Sangalli, G and V{\'a}zquez, R},
	Journal = {Mathematical Models and Methods in Applied Sciences},
	Number = {11},
	Pages = {1979--2003},
	Publisher = {World Scientific},
	Title = {Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties},
	Volume = {23},
	Year = {2013}}

@article{Bressan201517,
	Abstract = {Abstract In this article we provide the characterization of analysis suitable T-spline spaces (Beir{\~a}o da Veiga et al., 2013) as the space of piecewise polynomials with appropriate linear constrains on the subdomain interfaces. We describe AST-meshes for which the linear constrains are equivalent to smoothness conditions and provide examples showing that this is not always the case. },
	Author = {Andrea Bressan and Annalisa Buffa and Giancarlo Sangalli},
	Doi = {http://dx.doi.org/10.1016/j.cagd.2015.06.007},
	Issn = {0167-8396},
	Journal = {Computer Aided Geometric Design},
	Keywords = {Computer aided design},
	Pages = {17 - 49},
	Title = {Characterization of analysis-suitable T-splines},
	Url = {http://www.sciencedirect.com/science/article/pii/S0167839615000850},
	Volume = {39},
	Year = {2015},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167839615000850},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cagd.2015.06.007}}

@article{ZhangLi-16-TSplines,
	Author = {J. Zhang and X. Li},
	Doi = {http://dx.doi.org/10.1016/j.cagd.2016.05.010},
	Issn = {0167-8396},
	Journal = {Computer Aided Geometric Design},
	Pages = {16 - 29},
	Title = {On degree elevation of {T}-splines},
	Url = {http://www.sciencedirect.com/science/article/pii/S0167839616300656},
	Volume = {46},
	Year = {2016},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0167839616300656},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.cagd.2016.05.010}}

@article{scott2012local,
	Author = {Scott, MA and Li, X and Sederberg, TW and Hughes, TJR},
	Journal = {Computer Methods in Applied Mechanics and Engineering},
	Pages = {206--222},
	Publisher = {Elsevier},
	Title = {Local refinement of analysis-suitable T-splines},
	Volume = {213},
	Year = {2012}}

@article{Wang2015,
	Abstract = {One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational B-spline (NURBS). NURBS patches are the tensor product of one-dimensional NURBS, making the construction of arbitrary surfaces difficult. Trimmed NURBS use curves to trim away regions of the patch to obtain the desired shape. By coupling trimmed NURBS with a nonsingular BEM, the formulation proposed here comes close achieving the goal of direct design to analysis. Example calculations demonstrate its efficiency and accuracy.},
	Author = {Wang, Yingjun and Benson, David J. and Nagy, Attila P.},
	Doi = {10.1007/s00466-015-1165-y},
	Issn = {1432-0924},
	Journal = {Computational Mechanics},
	Number = {1},
	Pages = {173--191},
	Title = {A multi-patch nonsingular isogeometric boundary element method using trimmed elements},
	Url = {http://dx.doi.org/10.1007/s00466-015-1165-y},
	Volume = {56},
	Year = {2015},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00466-015-1165-y}}

@article{XFEM,
	Author = {Mo{\"e}s, Nicolas and Dolbow, John and Belytschko, Ted},
	Doi = {10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J},
	Issn = {1097-0207},
	Journal = {International Journal for Numerical Methods in Engineering},
	Keywords = {finite elements, fracture},
	Number = {1},
	Pages = {131--150},
	Publisher = {John Wiley & Sons, Ltd.},
	Title = {A finite element method for crack growth without remeshing},
	Url = {http://dx.doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J},
	Volume = {46},
	Year = {1999},
	Bdsk-Url-1 = {http://dx.doi.org/10.1002/(SICI)1097-0207(19990910)46:1%3C131::AID-NME726%3E3.0.CO;2-J}}

@article{rong2014efficiency,
	Author = {Rong, Junjie and Wen, Lihua and Xiao, Jinyou},
	Journal = {Engineering Analysis with Boundary Elements},
	Pages = {83--93},
	Publisher = {Elsevier},
	Title = {Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements},
	Volume = {38},
	Year = {2014}}

@article{guiggiani1992general,
	Author = {Guiggiani, M. and Krishnasamy, G. and Rudolphi, T.J. and Rizzo, F.J.},
	Journal = {Journal of Applied Mechanics},
	Number = {3},
	Pages = {604--614},
	Publisher = {ASME},
	Title = {A general algorithm for the numerical solution of hypersingular boundary integral equations},
	Volume = {59},
	Year = {1992}}

@article{rice1968path,
	Author = {Rice, James R},
	Journal = {Journal of applied mechanics},
	Number = {2},
	Pages = {379--386},
	Publisher = {American Society of Mechanical Engineers},
	Title = {A path independent integral and the approximate analysis of strain concentration by notches and cracks},
	Volume = {35},
	Year = {1968}}

@article{Stern1976,
	Abstract = {A path independent contour integral formula for the distinct calculation of combined mode stress intensity factors in linear plane elasticity problems is presented. The method is based on a Somigliana type singular integral representation and is easily appended to existing finite element computer codes. Numerical results to three problems with known perturbation solutions are given and demonstrate the accuracy and stability of the method.},
	Author = {Stern, M. and Becker, E. B. and Dunham, R. S.},
	Doi = {10.1007/BF00032831},
	Issn = {1573-2673},
	Journal = {International Journal of Fracture},
	Number = {3},
	Pages = {359--368},
	Title = {A contour integral computation of mixed-mode stress intensity factors},
	Url = {http://dx.doi.org/10.1007/BF00032831},
	Volume = {12},
	Year = {1976},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF00032831}}

@article{WEN1995450,
	Abstract = {A contour integral is proposed for the evaluation of stress intensity factors. The integral utilizes the exact solution of a loaded crack in an infinite sheet as an auxiliary solution. The advantage of this new path-independent integral is that it yields directly the opening mode and sliding mode stress intensity factors. This integral in used together with an indirect boundary element method to calculate stress intensity factors for several cracked configurations.},
	Author = {P.H. Wen and M.H. Aliabadi and D.P. Rooke},
	Doi = {http://dx.doi.org/10.1016/0307-904X(95)00009-9},
	Issn = {0307-904X},
	Journal = {Applied Mathematical Modelling},
	Keywords = {fracture mechanics},
	Number = {8},
	Pages = {450 - 455},
	Title = {A contour integral for the evaluation of stress intensity factors},
	Url = {http://www.sciencedirect.com/science/article/pii/0307904X95000099},
	Volume = {19},
	Year = {1995},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0307904X95000099},
	Bdsk-Url-2 = {http://dx.doi.org/10.1016/0307-904X(95)00009-9}}

@article{chen1999,
	Author = {Chen JT and Hong HK},
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@article{xu13jcp,
title = "Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method",
journal = "Journal of Computational Physics",
volume = "252",
number = "",
pages = "275 - 289",
year = "2013",
note = "",
issn = "0021-9991",
doi = "http://dx.doi.org/10.1016/j.jcp.2013.06.029",
url = "http://www.sciencedirect.com/science/article/pii/S0021999113004592",
author = "Gang Xu and Bernard Mourrain and Régis Duvigneau and André Galligo",
keywords = "Isogeometric analysis",
keywords = "Grid generation",
keywords = "Harmonic mapping",
keywords = "Variational method",
keywords = "Analysis-suitable parameterization"
}

@article{xu13cada,
title = "Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications",
journal = "Computer-Aided Design",
volume = "45",
number = "2",
pages = "395 - 404",
year = "2013",
note = "Solid and Physical Modeling 2012",
issn = "0010-4485",
doi = "http://dx.doi.org/10.1016/j.cad.2012.10.022",
url = "http://www.sciencedirect.com/science/article/pii/S0010448512002278",
author = "Gang Xu and Bernard Mourrain and Régis Duvigneau and André Galligo",
keywords = "Isogeometric analysis",
keywords = "Volume parameterization",
keywords = "Multi-block computational domain",
keywords = "Heat conduction"
}

@article{xu13cadb,
title = "Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis",
journal = "Computer-Aided Design",
volume = "45",
number = "4",
pages = "812 - 821",
year = "2013",
note = "Geometric Modeling and Processing 2010",
issn = "0010-4485",
doi = "http://dx.doi.org/10.1016/j.cad.2011.05.007",
url = "http://www.sciencedirect.com/science/article/pii/S0010448511001175",
author = "Gang Xu and Bernard Mourrain and Régis Duvigneau and André Galligo",
keywords = "Isogeometric analysis",
keywords = "Analysis-aware parameterization of computational domain",
keywords = "Injectivity",
keywords = "Shape optimization",
keywords = "Steepest descent method"
}

@article{xu17cad,
title = "Isogeometric computation reuse method for complex objects with topology-consistent volumetric parameterization ",
journal = "Computer-Aided Design ",
volume = "91",
number = "",
pages = "1 - 13",
year = "2017",
note = "",
issn = "0010-4485",
doi = "https://doi.org/10.1016/j.cad.2017.04.002",
url = "http://www.sciencedirect.com/science/article/pii/S0010448517300477",
author = "Gang Xu and Tsz-Ho Kwok and Charlie C.L. Wang",
keywords = "Computation reuse",
keywords = "Isogeometric analysis",
keywords = "Consistent volume parameterization "
}

 