ICAP 2002 Abstracts and Posters
Enhancements to the Iterative Inexact Lanczos Method for Solving Computationally Large Finite Element Eigenmode Problems
Abstract
The inexact Lanczos method implemented in Omega3P[1] is a
highly efficient technique for solving large generalized
eigenmode problems on parallel computers. For large finite
element problems the iterative solution of the shifted
linear system using the PCG method dominates the
computational time. Recent work has shown that the
convergence rate of PCG can be greatly enhanced by
introducing scalar degrees of freedom representing the
electric potential (the A-V method[2]). This paper
presents the implementation and application of the inexact
Lanczos method with A-V basis functions in the parallel
OM3P solver. Results for large RF cavity problems (> 1
million DOFs) demonstrate significant reductions in
computational time (more than a factor of 10 in some cases)
as compared to the original implementation. We have also
added a deflation algorithm that improves the performance
of the procedure on mode clusters, and the application of
this extension is illustrated.
[1] Y. Sun, N. Folwell, Z. Li, and G. Golub, "High
precision accelerator cavity design using the parallel
eigensolver Omega3P," Proceedings of The Annual Review of
Progress in Applied Computational Electromagnetics 2002.
[2] R. Dyczij-Edlinger, G. Peng, and J. F. Lee, "A fast
vector-potential method using tangentially continuous
vector finite elements," IEEE-MTT, 46, June, 1998,
pp.863-868.
John F. DeFord, Ben L. Held,
Simulation Technology & Applied Research, Inc.
11520 N. Port Washington Rd., Suite 101B
Mequon, WI 53092
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