A parallel subdomain by subdomain implementation of the implicitly restarted Arnoldi/Lanczos method

Authors:
G. O. Ainsworth, Jr.;F. L. Ribeiro;C. Magluta
Affiliations:
Programa de Engenharia Civil, COPPE/Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil 21945-970;Programa de Engenharia Civil, COPPE/Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil 21945-970;Programa de Engenharia Civil, COPPE/Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil 21945-970
Venue:
Computational Mechanics
Year:
2011

Citing 17
Cited 0

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Implicit application of polynomial filters in a k-step Arnoldi method

SIAM Journal on Matrix Analysis and Applications
Preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problems

SIAM Journal on Numerical Analysis
Analysis and implementation of an implicitly restarted Arnoldi iteration

Analysis and implementation of an implicitly restarted Arnoldi iteration
A high-performance, portable implementation of the MPI message passing interface standard

Parallel Computing
Implicitly restarted Arnoldi with purification for the shift-invert transformation

Mathematics of Computation
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Efficient management of parallelism in object-oriented numerical software libraries

Modern software tools for scientific computing
Implicitly Restarted Arnoldi Methods and Subspace Iteration

SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Study of a non-overlapping domain decomposition method: poisson and stokes problems

Applied Numerical Mathematics
Multiple Explicitly Restarted Arnoldi Method for Solving Large Eigenproblems

SIAM Journal on Scientific Computing
On a parallel multilevel preconditioned Maxwell eigensolver

Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Parallel Arnoldi eigensolvers with enhanced scalability via global communications rearrangement

Parallel Computing
Anasazi software for the numerical solution of large-scale eigenvalue problems

ACM Transactions on Mathematical Software (TOMS)
MPI-based parallel finite element approaches for implicit nonlinear dynamic analysis employing sparse PCG solvers

Advances in Engineering Software
Improving the parallel performance of a domain decomposition preconditioning technique in the Jacobi-Davidson method for large scale eigenvalue problems

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This work presents a parallel implementation of the implicitly restarted Arnoldi/Lanczos method for the solution of eigenproblems approximated by the finite element method. The implicitly restarted Arnoldi/Lanczos uses a restart scheme in order to improve the convergence of the desired portion of the spectrum, addressing issues such as memory requirements and computational costs related to the generation and storage of the Krylov basis. The presented implementation is suitable for distributed memory architectures, especially PC clusters. In the parallel solution, a subdomain by subdomain approach was implemented and overlapping and non-overlapping mesh partitions were tested. Compressed data structures in the formats CSRC and CSRC/CSR were used to store the coefficient matrices. The parallelization of numerical linear algebra operations present in both Krylov and implicitly restarted methods are discussed. Numerical examples are shown, in order to point out the efficiency and applicability of the proposed method.