721 citations · 1.8k across the 37 of their papers we have counts for
39 papers
A short perspective on a posteriori error control and adaptive discretizations
Roland Becker, Stéphane P. A. Bordas, Franz Chouly +1
Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since the…
Volume and Mass Conservation in Lagrangian Meshfree Methods
Pratik Suchde, Christian Leithäuser, Jörg Kuhnert +1
Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass c…
Breast simulation pipeline: from medical imaging to patient-specific simulations
Arnaud Mazier, Stéphane P. A. Bordas
Breast-conserving surgery is the most acceptable operation for breast cancer removal from an invasive and psychological point of view. Before the surgical procedure, a preoperative…
Level set topology optimization of metamaterial-based heat manipulators using isogeometric analysis
Chintan Jansari, Stéphane P. A. Bordas, Elena Atroshchenko
We exploit level set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level set function, geometry, and solution field…
Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanics
Saurabh Deshpande, Raúl I. Sosa, Stéphane P. A. Bordas +1
Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use…
MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations
Saurabh Deshpande, Stéphane P. A. Bordas, Jakub Lengiewicz
In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, d…
Smart cloud collocation: geometry-aware adaptivity directly from CAD
Thibault Jacquemin, Pratik Suchde, Stéphane P. A. Bordas
Computer Aided Design (CAD) is widely used in the creation and optimization of various industrial systems and processes. Transforming a CAD geometry into a computational discretiza…
SOniCS: Develop intuition on biomechanical systems through interactive error controlled simulations
Arnaud Mazier, Sidaty El Hadramy, Jean-Nicolas Brunet +3
This new approach allows the user to experiment with model choices easily and quickly without requiring in-depth expertise, as constitutive models can be modified by one line of co…
An a posteriori error estimator for the spectral fractional power of the Laplacian
Raphaël Bulle, Olga Barrera, Stéphane P. A. Bordas +2
We develop a novel a posteriori error estimator for the error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori err…
An adapted deflated conjugate gradient solver for robust extended/generalised finite element solutions of large scale, 3D crack propagation problems
Konstantinos Agathos, Tim Dodwell, Eleni Chatzi +1
An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned…
Probabilistic Deep Learning for Real-Time Large Deformation Simulations
Saurabh Deshpande, Jakub Lengiewicz, Stéphane P. A. Bordas
For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too…
Machine learning in the social and health sciences
Anja K. Leist, Matthias Klee, Jung Hyun Kim +4
The uptake of machine learning (ML) approaches in the social and health sciences has been rather slow, and research using ML for social and health research questions remains fragme…
A rigged model of the breast for preoperative surgical planning
Arnaud Mazier, Sophie Ribes, Benjamin Gilles +2
In breast surgical practice, drawing is part of the preoperative planning procedure and is essential for a successful operation. In this study, we design a pipeline to assist surge…
Inverse deformation analysis: an experimental and numerical assessment using the FEniCS Project
Arnaud Mazier, Alexandre Bilger, Antonio E. Forte +25
In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging…
Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Raphaël Bulle, Jack S. Hale, Alexei Lozinski +2
In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann pr…
A Bayesian multiscale CNN framework to predict local stress fields in structures with microscale features
Vasilis Krokos, Viet Bui Xuan, Stéphane P. A. Bordas +2
Multiscale computational modelling is challenging due to the high computational cost of direct numerical simulation by finite elements. To address this issue, concurrent multiscale…
Taylor-series expansion based numerical methods: a primer, performance benchmarking and new approaches for problems with non-smooth solutions
Thibault Jacquemin, Satyendra Tomar, Konstantinos Agathos +2
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking…
Quantifying discretization errors for soft-tissue simulation in computer assisted surgery: a preliminary study
Michel Duprez, Stéphane P. A. Bordas, Marek Bucki +7
Errors in biomechanics simulations arise from modeling and discretization. Modeling errors are due to the choice of the mathematical model whilst discretization errors measure the…
Isogeometric analysis with local adaptivity based on a posterior error estimation for elastodynamics
Peng Yu, Cosmin Anitescu, Satyendra Tomar +2
This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner-Mindlin plates. The adaptive discretization is based on…
Corotational Cut Finite Element Method for real-time surgical simulation: application to needle insertion simulation
Huu Phuoc Bui, Satyendra Tomar, Stéphane P. A. Bordas
This paper describes the use of the corotational cut Finite Element Method (FEM) for real-time surgical simulation. Users only need to provide a background mesh which is not necess…
Skew-symmetric Nitsche's formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact
Qingyuan Hu, Franz Chouly, Ping Hu +2
A simple skew-symmetric Nitsche's formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential bo…
Isogeometric analysis of thin Reissner-Mindlin plates and shells: locking phenomena and B-bar method
Qingyuan Hu, Yang Xia, Sundararajan Natarajan +3
We propose a local type of B-bar formulation, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic str…
Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT)
Elena Atroshchenko, Gang Xu, Satyendra Tomar +1
This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for appro…
Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation
Huu Phuoc Bui, Satyendra Tomar, Hadrien Courtecuisse +3
We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, includ…