A robust two-level domain decomposition preconditioner for systems of PDEs

Domain decomposition method of stochastic PDEs: a two-level scalable preconditioner

A Robust Two Level Domain Decomposition Preconditioner for Systems of PDEs Une Méthode de Décomposition de Domaine à Deux Niveaux Robuste pour les Systèmes d’EDPs

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such hete...

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...

A domain decomposition method of stochastic PDEs: An iterative solution techniques using a two-level scalable preconditioner

Recent advances in high performance computing systems and sensing technologies motivate computational simulations with extremely high resolution models with capabilities to quantify uncertainties for credible numerical predictions. A two-level domain decomposition method is reported in this investigation to devise a linear solver for the large-scale system in the Galerkin spectral stochastic fi...

A Multilevel Preconditioner for Domain Decomposition Boundary Systems

In this note, we consider multilevel preconditioning of the reduced boundary systems which arise in non-overlapping domain decomposition methods. It will be shown that the resulting preconditioned systems have condition numbers which are bounded in the case of multilevel spaces on the whole domain and grow at most proportional to the number of levels in the case of multilevel boundary spaces wi...