Additive schur complement approximation for elliptic problems with oscillatory coefficients

Authors:
J. Kraus
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria
Venue:
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
Year:
2011

Citing 2
Cited 0

Preconditioning of Boundary Value Problems Using Elementwise Schur Complements

SIAM Journal on Matrix Analysis and Applications
Element-by-Element schur complement approximations for general nonsymmetric matrices of two-by-two block form

LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing

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Abstract

We introduce an algorithm for Additive Schur Complement Approximation (ASCA) that can be used in various iterative methods for solving systems of linear algebraic equations arising from finite element discretization of Partial Differential Equations (PDE). Here we consider a model problem of a scalar elliptic PDE with highly oscillatory (piecewise constant) diffusion coefficient. The main ideas are illustrated by three different examples that reveal the key point of constructing a robust sparse ASCA. We also demonstrate how the quality of the ASCA can be improved and how its sparsity is controlled.