Publication
Conservation of Forces and Total Work at the Interface Using the Internodes Method
Publications associées (118)
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In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems wi ...
New York2024On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...
ELSEVIER SCIENCE INC2023Low-Rank Tensor Methods for High-Dimensional Problems
In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...
EPFL2023Testing Benchmark for a Block Conjugate Gradient Solving Scheme in Poroelasticity
With the advancement in fields of science more complex and more coupled phenomena can be explained, calculated and predicted. To solve these problems one has to update the related tools. Since analytical solutions do not exist for all physical processes, s ...
2023Explicit Stabilized Multirate Method For Stiff Differential Equations
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Stabilized Runge???Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge???Kutta me ...
AMER MATHEMATICAL SOC2022PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology
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In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...
2022Adaptive analysis-aware defeaturing
Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, ...
EPFL2022A Least-Squares Method for the Solution of the Non-smooth Prescribed Jacobian Equation
Alexandre Caboussat, Dimitrios Gourzoulidis
We consider a least-squares/relaxation finite element method for the numerical solution of the prescribed Jacobian equation. We look for its solution via a least-squares approach. We introduce a relaxation algorithm that decouples this least-squares proble ...
SPRINGER/PLENUM PUBLISHERS2022Spectral Coarse Spaces for the Substructured Parallel Schwarz Method
The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...
2022Fast global spectral methods for three-dimensional partial differential equations
Daniel Kressner, Christoph Max Strössner
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...
OXFORD UNIV PRESS2022