|Preprint-No.:||< 390 >||Published in:||March 2014||PDF-File:||IGPM390.pdf|
|Title:||Solving an Elliptic PDE Eigenvalue Problem via Automated Multi-Level Substructuring and Hierarchical Matrices|
|Authors:||Peter Gerds, Lars Grasedyck|
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|
|Most recent Version:||CLICK HERE|
|Publication:||Computing and Visualization in Science |
December 2013, Volume 16, Issue 6, pp 283-302