Additive Schur Complement Approximation for Elliptic Problems with Oscillatory Coefficients

  • J. Kraus
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)


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.


Linear Algebraic Equation Uniform Mesh Piecewise Constant Macro Structure Bilinear Element 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • J. Kraus
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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