TY  - GEN
T1  - Hierarchical Cholesky decomposition of sparse matrices arising from curl-curl-equation
A1  - Ibragimow,Ilgis
A1  - Rjasanow,Sergej
A1  - Straube,Katharina
Y1  - 2012/02/24
N2  - A new hierarchical renumbering technique for sparse matrices arising from the application of the Finite Element Method (FEM) to three-dimensional Maxwell's equations is presented. It allows the complete Cholesky decomposition of the matrix, which leads to a direct solver of O(N^{4/3}) 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.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4622
ER  -