Novel corrector problems with exponential decay of the resonance error for numerical homogenization
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.
The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...
In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...
In this work we compare numerically different families of nested quadrature points, i.e. the classic Clenshaw{Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence ...
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 ...
In this thesis we study the efficient implementation of the finite element method for the numerical solution of partial differential equations (PDE) on modern parallel computer archi- tectures, such as Cray and IBM supercomputers. The domain-decomposition ...
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 ...
In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the s ...
The goal of this report is to study the method introduced by Adomian known as the Adomian Decomposition Method (ADM), which is used to find an approximate solution to nonlinear partial differential equations (PDEs) as a series expansion involving the recur ...
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 ...
This work focuses on the finite element discretization of boundary value problems whose solution features either a discontinuity or a discontinuous conormal derivative across an interface inside the computational domain. The interface is characterized via ...
