Additive Schur Complement Approximation for Elliptic Problems with Oscillatory Coefficients
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.
KeywordsLinear Algebraic Equation Uniform Mesh Piecewise Constant Macro Structure Bilinear Element
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