Domain decomposition for multiscale PDEs

Domain decomposition for multiscale PDEs

We consider additive Schwarz domain decomposition preconditioners for piecewise linear finite element approximations of elliptic PDEs with highly variable coefficients. In contrast to standard analyses, we do not assume that the coefficients can be resolved by a coarse mesh. This situation arises often in practice, for example in the computation of flows in heterogeneous porous media, in both t...

Robust Domain Decomposition Algorithms for Multiscale PDEs

In this paper we describe a new class of domain deomposition preconditioners suitable for solving elliptic PDEs in highly fractured or heterogeneous media, such as arise in groundwater flow or oil recovery applications. Our methods employ novel coarsening operators which are adapted to the heterogeneity of the media. In contrast to standard methods (based on piecewise polynomial coarsening), th...

Domain decomposition preconditioners for multiscale problems

In this paper, we study domain decomposition preconditioners for multiscale elliptic problems in high contrast media. We construct preconditioners such that the condition number of the preconditioned system is independent of media contrast. For this purpose, multiscale spaces for the interpolation on the coarse grid is developed using a local weighted spectral problem. A main observation is tha...

New constructions of domain decomposition methods for systems of PDEs

Scalable Parallel Domain Decomposition Methods for Numerical Simulation of PDEs

This paper is concerned about scalable parallel domain decomposition methods for numerical simulation of PDEs. First, one level and two level scalable parallel domain decomposition methods which can be used to solve different equations, are introduced in detail, and then we explain Krylov subspace accelerator technique used to improve the convergence of the methods. Last, the results of some nu...