Jacquemin, T., Tomar, S., Agathos, K., Mohseni-Mofidi, S., Bordas, S., Taylor-series expansion based numerical methods: A primer, performance benchmarking and new approaches for problems with non-smooth solutions. Arch Comput Methods Eng, 2019, 10.1007/s11831-019-09357-5.
Jacquemin, T., Bordas, S.P.A., A unified algorithm for the selection of collocation stencils for convex, concave and singular problems. Internat J Numer Methods Engrg, 2021, 10.1002/nme.6703.
Liszka, T., Orkisz, J., The finite difference method at arbitrary irregular grids and its application in applied mechanics. Comput Struct 11:1–2 (1980), 83–95, 10.1016/0045-7949(80)90149-2.
Benito, J., Ureña, F., Gavete, L., Influence of several factors in the generalized finite difference method. Appl Math Model 25:12 (2001), 1039–1053, 10.1016/s0307-904x(01)00029-4.
Milewski, S., Meshless finite difference method with higher order approximation—applications in mechanics. Arch Comput Methods Eng 19:1 (2012), 1–49, 10.1007/s11831-012-9068-y.
Shepard, D., A two-dimensional interpolation function for irregularly-spaced data. Proceedings of the 1968 23rd ACM national conference, 1968, ACM Press, 517–524, 10.1145/800186.810616.
Lancaster, P., Salkauskas, K., Surfaces generated by moving least squares methods. Math Comp, 37(155), 1981, 141, 10.1090/s0025-5718-1981-0616367-1.
Oñate, E., Idelsohn, S., Zienkiewick, O., Taylor, R., A finite point method in computational mechanics. Application to convective transport and fluid flow. Internat J Numer Methods Engrg 39:22 (1996), 3839–3866, 10.1002/(sici)1097-0207(19961130)39:22<3839::aid-nme27>3.0.co;2-r.
Kansa, E., Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—i surface approximations and partial derivative estimates. Comput Math Appl 19:8–9 (1990), 127–145, 10.1016/0898-1221(90)90270-t.
Kansa, E., Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19:8–9 (1990), 147–161, 10.1016/0898-1221(90)90271-k.
Driscoll, T., Fornberg, B., Interpolation in the limit of increasingly flat radial basis functions. Comput Math Appl 43:3–5 (2002), 413–422, 10.1016/s0898-1221(01)00295-4.
Davydov, O., Oanh, D.T., On the optimal shape parameter for Gaussian radial basis function finite difference approximation of the Poisson equation. Comput Math Appl 62:5 (2011), 2143–2161, 10.1016/j.camwa.2011.06.037.
Politis, C., Ginnis, A.I., Kaklis, P.D., Belibassakis, K., Feurer, C., An isogeometric BEM for exterior potential-flow problems in the plane. 2009 SIAM/ACM joint conference on geometric and physical modeling on - SPM '09, 2009, ACM Press, 10.1145/1629255.1629302.
Belibassakis, K.A., Gerostathis, T.P., Kostas, K.V., Politis, C.G., Kaklis, P.D., Ginnis, A.I., et al. A BEM-isogeometric method with application to the wavemaking resistance problem of ships at constant speed. Volume 6: Ocean engineering, 2011, ASMEDC, 10.1115/omae2011-49159.
Simpson, R., Bordas, S., Trevelyan, J., Rabczuk, T., A two-dimensional isogeometric boundary element method for elastostatic analysis. Comput Methods Appl Mech Engrg 209–212 (2012), 87–100, 10.1016/j.cma.2011.08.008.
Ginnis, A.I., Feurer, C., Belibassakis, K., Kaklis, P.D., Kostas, K., Gerostathis, T.P., et al. A CATIA ship-parametric model for isogeometric hull optimization with respect to wave resistance. 2015.
Lian, H., Simpson, R., Bordas, S., Stress analysis without meshing: Isogeometric boundary-element method. Proc Inst Civ Eng - Eng Comput Mech 166:2 (2013), 88–99, 10.1680/eacm.11.00024.
Simpson, R., Scott, M., Taus, M., Thomas, D., Lian, H., Acoustic isogeometric boundary element analysis. Comput Methods Appl Mech Engrg 269 (2014), 265–290, 10.1016/j.cma.2013.10.026 URL https://www.sciencedirect.com/science/article/pii/S0045782513002788.
Peng, X., Atroshchenko, E., Kerfriden, P., Bordas, S., Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth. Comput Methods Appl Mech Engrg 316 (2017), 151–185, 10.1016/j.cma.2016.05.038.
Lian, H., Kerfriden, P., Bordas, S., Shape optimization directly from CAD: An isogeometric boundary element approach using T-splines. Comput Methods Appl Mech Engrg 317 (2017), 1–41, 10.1016/j.cma.2016.11.012.
Auricchio, F., da Veiga, L.B., Hughes, T., Reali, A., Sangalli, G., Isogeometric collocation methods. Math Models Methods Appl Sci 20:11 (2010), 2075–2107, 10.1142/s0218202510004878.
Benito, J.J., Urena, F., Gavete, L., Alonso, B., A posteriorierror estimator and indicator in generalized finite differences. Application to improve the approximated solution of elliptic PDEs. Int J Comput Math 85:3–4 (2008), 359–370, 10.1080/00207160601167052.
Gavete, L., Gavete, M.L., Ureña, F., Benito, J.J., An approach to refinement of irregular clouds of points using generalized finite differences. Math Probl Eng 2015 (2015), 1–9, 10.1155/2015/283757.
Suchde, P., Kuhnert, J., A meshfree generalized finite difference method for surface PDEs. Comput Math Appl 78:8 (2019), 2789–2805, 10.1016/j.camwa.2019.04.030 URL http://www.sciencedirect.com/science/article/pii/S0898122119302469.
Davydov, O., Oanh, D.T., Adaptive meshless centres and RBF stencils for Poisson equation. J Comput Phys 230:2 (2011), 287–304, 10.1016/j.jcp.2010.09.005.
Oanh, D.T., Davydov, O., Phu, H.X., Adaptive RBF-FD method for elliptic problems with point singularities in 2D. Appl Math Comput 313 (2017), 474–497, 10.1016/j.amc.2017.06.006 URL https://www.sciencedirect.com/science/article/pii/S0096300317304186.
Slak, J., Adaptive RBF-FD method. [Ph.D. thesis], 2020, Univerza v Ljubljani, Fakulteta za matematiko in fiziko.
Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S., A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J Comput Phys 152:2 (1999), 457–492, 10.1006/jcph.1999.6236.
Runnels, B., Agrawal, V., Zhang, W., Almgren, A., Massively parallel finite difference elasticity using block-structured adaptive mesh refinement with a geometric multigrid solver. J Comput Phys, 427, 2021, 110065, 10.1016/j.jcp.2020.110065.
OpenCASCADE: Open CASCADE technology, 3D modeling & numerical simulation, https://dev.opencascade.org/.
Geuzaine, C., Remacle, J.-F., Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. Internat J Numer Methods Engrg 79:11 (2009), 1309–1331, 10.1002/nme.2579.
Löhner, R., Oñate, E., An advancing front point generation technique. Commun Numer Methods Eng 14:12 (1998), 1097–1108, 10.1002/(sici)1099-0887(199812)14:12<1097::aid-cnm183>3.0.co;2-7.
Shimrat, M., Algorithm 112: Position of point relative to polygon. Commun ACM, 5(8), 1962, 434, 10.1145/368637.368653.
Chinn, W., Steenrod, N., First concepts of topology. 1966, The Mathematical Association of America, 10.5948/upo9780883859339.
O'Rourke, J., Computational geometry in C second edition (Cambridge tracts in theoretical computer science (Paperback)). 1998, Cambridge University Press URL https://www.xarg.org/ref/a/0521649765/.
Alliez, P., Tayeb, S., Wormser, C., 3D fast intersection and distance computation. CGAL user and reference manual, 5.0, 2019, CGAL Editorial Board URL https://doc.cgal.org/5.0/Manual/packages.html.
Gao, X.-L., A general solution of an infinite elastic plate with an elliptic hole under biaxial loading. Int J Press Vessels Pip 67:1 (1996), 95–104, 10.1016/0308-0161(94)00173-1.
Gould, P., Introduction to linear elasticity. 2013, Springer, New York.
Zienkiewicz, O.C., Zhu, J.Z., A simple error estimator and adaptive procedure for practical engineerng analysis. Internat J Numer Methods Engrg 24:2 (1987), 337–357, 10.1002/nme.1620240206.
Bordas, S., Duflot, M., Derivative recovery and a posteriori error estimate for extended finite elements. Comput Methods Appl Mech Engrg 196:35 (2007), 3381–3399, 10.1016/j.cma.2007.03.011 URL https://www.sciencedirect.com/science/article/pii/S0045782507001417.
Duflot, M., Bordas, S., A posteriorierror estimation for extended finite elements by an extended global recovery. Internat J Numer Methods Engrg 76:8 (2008), 1123–1138, 10.1002/nme.2332.
Ródenas, J.J., Duflot, M., Bordas, S., Giner, E., González-Estrada, O.A., Fuenmayor, F.J., Comparison of recently developed recovery type discretization error estimators for the extended finite element method. 8th World congress on computational mechanics (WCCM8). 5th. European congress on computational methods in applied sciences and engineering, 2008, CINME.
Driscoll, T., Heryudono, A., Adaptive residual subsampling methods for radial basis function interpolation and collocation problems. Comput Math Appl 53 (2007), 927–939.
Oh, J., Adaptive meshfree methods for partial differential equations. [Ph.D. thesis], 2018, University of Southern Mississippi.
Benito, J., Ureña, F., Gavete, L., Alvarez, R., An h-adaptive method in the generalized finite differences. Comput Methods Appl Mech Engrg 192:5–6 (2003), 735–759, 10.1016/s0045-7825(02)00594-7.
Jancic M, Slak J, Kosec G. p-refined RBF-FD solution of a Poisson problem. In: 2021 6th International conference on smart and sustainable technologies. 2021, p. 01–6.
Dorfler, W., A convergent adaptive algorithm for Poisson's equation. SIAM J Numer Anal 33:3 (1996), 1106–1124 URL http://www.jstor.org/stable/2158497.
Bulle, R., Hale, J.S., Lozinski, A., Bordas, S.P.A., Chouly, F., Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS project. 2021 ArXiv, arXiv:2102.04360.
Electricité de France. Finite element code_aster, analysis of structures and thermomechanics for studies and research. Open source on https://www.code-aster.org.
Suchde, P., Kuhnert, J., Tiwari, S., On meshfree GFDM solvers for the incompressible Navier–Stokes equations. Comput & Fluids 165 (2018), 1–12, 10.1016/j.compfluid.2018.01.008 URL http://www.sciencedirect.com/science/article/pii/S0045793018300070.
Lian, H., Kerfriden, P., Bordas, S.P.A., Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Internat J Numer Methods Engrg 106:12 (2016), 972–1017, 10.1002/nme.5149.
Chen, L., Lian, H., Liu, Z., Chen, H., Atroshchenko, E., Bordas, S., Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods. Comput Methods Appl Mech Engrg 355 (2019), 926–951, 10.1016/j.cma.2019.06.012.
Chen, L., Lu, C., Lian, H., Liu, Z., Zhao, W., Li, S., et al. Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods. Comput Methods Appl Mech Engrg, 362, 2020, 112806, 10.1016/j.cma.2019.112806 URL https://www.sciencedirect.com/science/article/pii/S004578251930698X.
Chen, L., Zhang, Y., Lian, H., Atroshchenko, E., Ding, C., Bordas, S., Seamless integration of computer-aided geometric modeling and acoustic simulation: Isogeometric boundary element methods based on Catmull-Clark subdivision surfaces. Adv Eng Softw, 149, 2020, 102879, 10.1016/j.advengsoft.2020.102879 URL https://www.sciencedirect.com/science/article/pii/S0965997820305779.
Thakur, A., Banerjee, A.G., Gupta, S.K., A survey of CAD model simplification techniques for physics-based simulation applications. Comput Aided Des 41:2 (2009), 65–80, 10.1016/j.cad.2008.11.009.
Danglade, F., Pernot, J.-P., Véron, P., On the use of machine learning to defeature CAD models for simulation. Comput-Aided Des Appl 11:3 (2013), 358–368, 10.1080/16864360.2013.863510.
Prudhomme, S., Oden, J., On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Comput Methods Appl Mech Engrg 176:1 (1999), 313–331, 10.1016/S0045-7825(98)00343-0 URL https://www.sciencedirect.com/science/article/pii/S0045782598003430.
Chamoin, L., Legoll, F., Goal-oriented error estimation and adaptivity in MsFEM computations. Comput Mech 67:4 (2021), 1201–1228, 10.1007/s00466-021-01990-x.
Aghighi, F., Ebadati, O., Aghighi, H., Classification of LiDAR points cloud using Markov random field and machine learning techniques. Iran J Remote Sens GIS 9:2 (2018), 41–60.
Aghighi, F., Aghighi, H., Ebadati, O.M., Conditional random fields for airborne lidar point cloud classification in urban area. Eng J Geospat Inf Technol 7:4 (2020), 139–156.
Li, L., Sung, M., Dubrovina, A., Yi, L., Guibas, L.J., Supervised fitting of geometric primitives to 3D point clouds. 2019 IEEE/CVF conference on computer vision and pattern recognition, 2019, IEEE, 10.1109/cvpr.2019.00276.
Angles, B., Geometric modeling with primitives. [Ph.D. thesis], 2019, Université Paul Sabatier -, Toulouse III.
Saporta, T., Sharf, A., Unsupervised recursive deep fitting of 3D primitives to points. Comput Graph, 2021, 10.1016/j.cag.2021.10.020 URL https://www.sciencedirect.com/science/article/pii/S0097849321002314.
Zhan, Q., Liang, Y., Xiao, Y., Color-based segmentation of point clouds. ISPRS Laser Scanning Workshop, vol. 38, 2009.
Awrangjeb, M., Zhang, C., Fraser, C.S., Automatic extraction of building roofs using LIDAR data and multispectral imagery. ISPRS J Photogram Remote Sens 83 (2013), 1–18, 10.1016/j.isprsjprs.2013.05.006.
Alshawabkeh, Y., Linear feature extraction from point cloud using color information. Heritage Sci, 8(1), 2020, 10.1186/s40494-020-00371-6.
Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., et al. PETSc users manual: Tech. rep. ANL-95/11 - Revision 3.9., 2018, Argonne National Laboratory.
Falgout, R.D., Yang, U.M., Hypre: A library of high performance preconditioners. Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J., (eds.) Computational science — ICCS 2002, 2002, Springer Berlin Heidelberg, Berlin, Heidelberg, 632–641.
The Trilinos Project Team. The trilinos project website.
Schroeder, W., The visualization toolkit: An object-oriented approach to 3D graphics. 2006, Kitware, Clifton Park, N.Y.
The CGAL Project, W., CGAL user and reference manual, 5.3.1. 2021, CGAL Editorial Board URL https://doc.cgal.org/5.3.1/Manual/packages.html.
Rycroft, C., VORO++: A three-dimensional VORONOI cell library in C++. Chaos, 19(4), 2009, 041111, 10.1063/1.3215722.
