A Purely Algebraic Approach to Preconditioning Based on Hierarchical LU Factorizations

M. Bebendorf and T. Fischer ()
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M. Bebendorf: University Leipzig, Mathematical Institute, Faculty of Mathematics and Computer Science
T. Fischer: University Leipzig, Mathematical Institute, Faculty of Mathematics and Computer Science

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 135-142 from Springer

Abstract: Abstract The efficiency of hierarchical matrices depends on the quality of the block partition. We describe a nested dissection partitioning of the matrix into blocks that uses only the matrix graph and requires a logarithmic-linear number of operations. This block partition allows to compute a hierarchical LU decomposition with small fill-in. Furthermore, the algebraic approach admits, in contrast to the usual geometric partitioning, general grids for finite element discretization of elliptic boundary value problems.

Date: 2008
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DOI: 10.1007/978-3-540-69777-0_15

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