Publication
Regularity And Selecting Principles For Implicit Ordinary Differential Equations
Publications associées (39)
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We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...
Elsevier2015Reduced basis heterogeneous multiscale methods
Numerical methods for partial differential equations with multiple scales that combine numerical homogenization methods with reduced order modeling techniques are discussed. These numerical methods can be applied to a variety of problems including multisca ...
2015Application aux équations aux dérivées partielles d'une méthode par point fixe et le problème des deux puits
This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form [ \mathcal Lu + \mathcal Q(u) = f.] The main result of thi ...
EPFL2015Isogeometric Analysis of Electrophysiological Models on Surfaces
In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-UniformRational B-Splines) basis ...
2014Optimal control for Partial Differential Equations
In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...
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Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...
Elsevier Science Sa2013BPX-preconditioning for isogeometric analysis
We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by ...
2013Coupling reduced basis and numerical homogenization methods for solving quasilinear elliptic problems
The workshop has brought together experts in the broad field of partial differential equations with highly heterogeneous coefficients. Analysts and computational and applied mathematicians have shared results and ideas on a topic of considerable interest b ...
EMS2013Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...
2013