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.
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© 2008 Springer-Verlag Berlin Heidelberg
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Bebendorf, M., Fischer, T. (2008). A Purely Algebraic Approach to Preconditioning Based on Hierarchical LU Factorizations. In: Kunisch, K., Of, G., Steinbach, O. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69777-0_15
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DOI: https://doi.org/10.1007/978-3-540-69777-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69776-3
Online ISBN: 978-3-540-69777-0
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