Reduced basis Nitsche-based domain decomposition: a biomedical application

Scientific Conference (2017, March 10)

Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity ... [more ▼]

Nowadays, the personalized biomedical simulations demand real-time efficient and reliable method to alleviate the computational complexity of high-fidelity simulation. In such applications, the necessity of solving different substructure, e.g. tissues or organs, with different numbers of the degrees of freedom and of coupling the reduced order spaces for each substructure poses a challenge in the on-fly simulation. In this talk, this challenge is taken into account employing the Nitsche-based domain decomposition technique inside the reduced order model [1]. This technique with respect to other domain decomposition approach allows obtaining a solution with the same accuracy of underlying finite element formulation and to flexibly treat interface with non-matching mesh. The robustness of the coupling is determined by the penalty coefficients that is chosen using ghost penalty technique [2]. Furthermore, to reduce the computational complexity of the on-fly assembling it is employed the empirical interpolation approach proposed in [3]. The numerical tests, performed using FEniCS[4], petsc4py and slepc4py [5], shows the good performance of the method and the reduction of computation cost. [1] Baroli, D., Beex L. and Bordas, S. Reduced basis Nitsche-based domain decomposition. In preparation. [2] Burman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2015). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. [3] E. Schenone, E., Beex,L., Hale, J.S., Bordas S. Proper Orthogonal Decomposition with reduced integration method. Application to nonlinear problems. In preparation. [4] A. Logg, K.-A. Mardal, G. N. Wells et al. Automated Solution of Differential Equations by the Finite Element Method, Springer 2012. [5] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011. http://dx.doi.org/10.1016/j.advwatres.2011.04.013 [less ▲]

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

in International Journal for Numerical Methods in Engineering (2017), 110(3), 203-226

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms ... [more ▼]

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrixes can be computed by smoothing technique. This is accomplished by combining the Green’s divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. [less ▲]

Programming the material point method in Julia

in Advances in Engineering Software (2017), 105

This article presents the implementation of the material point method (MPM) using Julia. Julia is an open source, multi-platform, high-level, high-performance dynamic programming language for technical ... [more ▼]

This article presents the implementation of the material point method (MPM) using Julia. Julia is an open source, multi-platform, high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to Matlab and Python programmers. MPM is a hybrid particle-grid approach that combines the advantages of Eulerian and Lagrangian methods and is suitable for complex solid mechanics problems involving contact, impact and large deformations. We will show that a Julia based MPM code, which is short, compact and readable and uses only Julia built in features, performs much better (with speed up of up to 8) than a similar Matlab based MPM code for large strain solid mechanics simulations. We share our experiences of implementing MPM in Julia and demonstrate that Julia is a very interesting platform for rapid development in the field of scientific computing. [less ▲]

Error-controlled adaptive extended finite element method for 3D linear elastic crack propagation

in Computer Methods in Applied Mechanics and Engineering (2017), 318

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique ... [more ▼]

We present a simple error estimation and mesh adaptation approach for 3D linear elastic crack propagation simulations using the eXtended Finite Element Method (X-FEM). A global extended recovery technique (Duflot and Bordas, 2008) is used to quantify the interpolation error. Based on this error distribution, four strategies relying on two different mesh optimality criteria are compared. The first aims at homogenizing the error distribution. The second minimizes the total number of elements given a target global error level. We study the behaviour of these criteria in the context of cracks treated by an X-FE approach. In particular, we investigate the convergence rates at the element-level depending its enrichment type. We conclude on the most suitable refinement criterion and propose and verify a strategy for mesh adaptation on 3D damage tolerance assessment problems. [less ▲]

A linear smoothed quadratic finite element for the analysis of laminated composite Reissner–Mindlin plates

in Composite Structures (2017), 180

It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by ... [more ▼]

It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by the shear-locking and distorted meshes for the plate problems. In this paper, a linear smoothed eight-node Reissner-Mindlin plate element (Q8 plate element) based on the first order shear deformation theory is developed for the static and free vibration analysis of laminated composite plates, the computation of the interior derivatives of shape function and isoparametric mapping can be removed. The strain matrices are modified with a linear smoothing technique by using the divergence theorem between the nodal shape functions and their derivatives in Taylor’s expansion. Moreover, the first order Taylor’s expansion is also employed for the construction of stiffness matrix to satisfy the linear strain distribution. Several numerical examples indicate that the novel Q8 plate element has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes. [less ▲]

An implicit potential method along with a meshless technique for incompressible fluid flows for regular and irregular geometries in 2D and 3D

in Engineering Analysis with Boundary Elements (2017), 77

We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state ... [more ▼]

We present the Implicit Potential (IPOT) numerical scheme developed in the framework of meshless point collocation. The proposed scheme is used for the numerical solution of the steady state, incompressible Navier-Stokes (N-S) equations in their primitive variable (u-v-w-p) formulation. The governing equations are solved in their strong form using either a collocated or a semi-staggered type meshless nodal configuration. The unknown field functions and derivatives are calculated using the Modified Moving Least Squares (MMLS) interpolation method. Both velocity-correction and pressure correction methods applied ensure the incompressibility constraint and mass conservation. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it can be applied, in a straightforward manner to: steady, unsteady, internal and external fluid flows in 2D and 3D, (ii) it equally applies to regular an irregular geometries, (iii) a distribution of points is sufficient, no numerical integration in space nor any mesh structure are required, (iv) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (v) it is quite simple and accurate, (vi) results can be obtained using collocated or semi-staggered nodal distributions, (vii) there is no need to compute the velocity potential nor the unit normal vectors and (viii) there is no need for a curvilinear system of coordinates. Simulations of fluid flow in 2D and 3D for regular and irregular geometries indicate the validity of the proposed methodology. [less ▲]

Image to analysis pipeline: single and double balloons kyphoplasty

Poster (2016, December 12)

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical ... [more ▼]

In this work, we present a semi-automatic pipeline from image to simulation of a patient fractured vertebra after the kyphoplastic augmentation with two balloons. In this procedure, the CT-scan medical image are pre-processed using open-source software Slice3D for segmentation and 3D reconstruction operation. Then, using geometric processing the 3D surface geometry is enhanced to avoid degenerate element and trigging phenomena on vertebra and cement area. We perform a finite element analysis to evaluate the risk of subsequent vertebral fracture. Finally using Monte-Carlo technique, we assess the propagation of uncertainty of material parameter on the evaluation of this risk. Based on the developed semi-automatic pipelines, it is possible to perform a patient-specific simulation that assesses the successful of kyphoplasty operation. [less ▲]

Shape Optimization Directly from CAD: an Isogeometric Boundary Element Approach Using T-splines

Report (2016)

Simulating topological changes in real time for surgical assistance

Speeches/Talks (2016)

Weakening the tight coupling between geometry and simulation in isogeometric analysis

Scientific Conference (2016, June 05)

In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry ... [more ▼]

In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is employed for the numerical solution of the problem over the domain. However, there are situations where this tight integration is a bane rather than a boon. Such situations arise where, e.g., (1) the geometry of the domain is simple enough to be represented by low order NURBS, whereas the unknown (exact) solution of the problem is sufficiently regular, and thus, the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry, (2) the constraint of using the same space for the geometry and the numerical solution is particularly undesirable, such as in the shape and topology optimization, and (3) the solution of the problem has low regularity but for the curved boundary of the domain one can employ higher order NURBS. Therefore, we propose to weaken this constraint. An extensive study of patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution will be discussed. It will be shown, with concrete reasoning, that why patch test fails in certain cases, and that those cases should be avoided in practice. Thereafter, selective numerical examples will be presented to address some of the above-mentioned situations, and it will be shown that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces, and thus, improved accuracy of the numerical solution. Powered by [less ▲]