Efficient solution of lattice equations by the recovery method Part I: Scalar elliptic problems

Abstract

In this paper, an efficient solver for high dimensional lattice equations will be introduced. We will present a new concept, the recovery method, to define a bilinear form on the continuous level which has equivalent energy as the original lattice equation. The finite element discretisation of the continuous bilinear form will lead to a stiffness matrix which serves as an quasi-optimal preconditioner for the lattice equations. Since a large variety of efficient solvers are available for linear finite element problems the new recovery method allows to apply these solvers for unstructured lattice problems.

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Correspondence to S.A. Sauter.

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G. Wittum

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Babuška, I., Sauter, S. Efficient solution of lattice equations by the recovery method Part I: Scalar elliptic problems. Comput. Visual Sci. 7, 113–119 (2004). https://doi.org/10.1007/s00791-004-0146-z

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Keywords

  • Bilinear Form
  • Element Discretisation
  • Lattice Equation
  • Multigrid Method
  • Recovery Method