Computing and Visualization in Science

, Volume 7, Issue 3–4, pp 113–119

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

• I. Babuška
• S.A. Sauter
Regular article

## 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.

## Keywords

Bilinear Form Element Discretisation Lattice Equation Multigrid Method Recovery Method
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