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Licensed Unlicensed Requires Authentication Published by De Gruyter August 15, 2007

Hierarchical Cholesky decomposition of sparse matrices arising from curl–curl-equation

  • I. Ibragimov , S. Rjasanow and K. Straube

A new hierarchical renumbering technique for sparse matrices arising from the application of the Finite Element Method (FEM) to the three-dimensional Maxwell's equations is presented. It allows the complete Cholesky decomposition of the matrix, which leads to a direct solver with O(N4/3) memory requirement. In addition, an approximate factorisation, yielding a preconditioner for the matrix, can be constructed. For this, two algorithms using low-rank approximation are presented, which have almost linear arithmetic complexity and memory requirement. The efficiency of the methods is demonstrated on several numerical examples.

Published Online: 2007-08-15
Published in Print: 2007-05-23

Copyright 2007, Walter de Gruyter

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