Algebraic Domain Decomposition Methods for Highly Heterogeneous Problems

Optimized algebraic interface conditions in domain decomposition methods for strongly heterogeneous unsymmetric problems

Under classical assumptions on the coefficients of the problem (e.g. η − 1 2divb > 0 a.e. in Ω) the matrix A in (2) is definite positive. We solve problem (2) by means of an Optimized Schwarz Method: such methods have been introduced at the continuous level in [4], and at the discrete level in [5]. We design optimized interface conditions directly at the algebraic level, in order to guarantee r...

Algebraic Domain Decomposition Methods for Darcy flow in heterogeneous media

A Two-Level Schwarz Preconditioner for Heterogeneous Problems

Coarse space correction is essential to achieve algorithmic scalability in domain decomposition methods. Our goal here is to build a robust coarse space for Schwarz–type preconditioners for elliptic problems with highly heterogeneous coefficients when the discontinuities are not just across but also along subdomain interfaces, where classical results break down [3, 6, 15, 9]. In previous work, ...

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...

Overlapping Domain Decomposition Algorithms for General Sparse Matrices

Domain decomposition methods for Finite Element problems using a partition based on the underlying nite element mesh have been extensively studied In this paper we discuss algebraic extensions of the class of overlapping domain decomposition algorithms for general sparse matrices The subproblems are created with an overlapping partition of the graph corresponding to the sparsity structure of th...