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Additive Schur Complement Approximation for Elliptic Problems with Oscillatory Coefficients

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7116)

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.

Keywords

  • Linear Algebraic Equation
  • Uniform Mesh
  • Piecewise Constant
  • Macro Structure
  • Bilinear Element

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Kraus, J. (2012). Additive Schur Complement Approximation for Elliptic Problems with Oscillatory Coefficients. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)