Stochastic spectral Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison
Graph Chatbot
Chat with Graph Search
Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
In focusing Kerr media, small- scale filamentation is the major obstacle to imaging at high light intensities. In this article, we experimentally and numerically demonstrate a method based on statistical averaging to reduce the detrimental effects of filam ...
Many applied problems, like transport processes in porous media or ferromagnetism in composite materials, can be modeled by partial differential equations (PDEs) with heterogeneous coefficients that rapidly vary at small scales. To capture the effective be ...
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...
A fully discrete analysis of the finite element heterogeneous multiscale method (FE-HMM) for elliptic problems with N+1 well-separated scales is discussed. The FE-HMM is a numerical homogenization method that relies on a macroscopic scheme (macro FEM) for ...
In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEM) for elliptic problems with highly oscillating coefficients. The method is based on multiscale finite element methods with local test functions that encode the oscillatory ...
Society for Industrial and Applied Mathematics2015
A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates becaus ...
In this paper we discuss the use of the sum-factorization for the calculation of the integrals arising in Galerkin isogeometric analysis. While introducing very little change in an isogeometric code based on element-by-element quadrature and assembling, th ...
Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Gal ...
Society for Industrial and Applied Mathematics2013
We study the approximation properties of a wide class of finite element differential forms on curvilinear cubic meshes in n dimensions. Specifically, we consider meshes in which each element is the image of a cubical reference element under a diffeomorphis ...
We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...
Society for Industrial and Applied Mathematics2014