390 IGPM390.pdf        March 2014
TITLE Solving an Elliptic PDE Eigenvalue Problem via Automated Multi-Level Substructuring and Hierarchical Matrices
AUTHORS Peter Gerds, Lars Grasedyck
ABSTRACT We propose a new method for the solution of discretised elliptic PDE eigen- value problems. The new method combines ideas of domain decomposition, as in the automated multi-level substructuring (short AMLS), with the concept of hierarchical matrices (short H-matrices) in order to obtain a solver that scales almost linearly (linear up to logarithmic factors) in the size of the discrete space. Whereas the AMLS method is very effective for PDEs posed in two dimensions, it is getting very expensive in the three-dimensional case, due to the fact that the interface coupling in the domain decomposition requires dense matrix operations. We resolve this problem by use of data-sparse hierarchical matrices. In addition to the discretisation error our new approach involves a projection error due to AMLS and an arithmetic error due to H-matrix approximation. A suitable choice of parameters to balance these errors is investigated in examples.
KEYWORDS automated multi-level substructuring, hierarchical matrices, elliptic PDE eigenvalue problem
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DOI 10.1007/s00791-015-0239-x
PUBLICATION Computing and Visualization in Science
December 2013, Volume 16, Issue 6, pp 283-302