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An Assessment of Parallel Preconditioners for the Interior Sparse Generalized Eigenvalue Problems by CG-type Methods on an IBM Regatta Machine

Title
An Assessment of Parallel Preconditioners for the Interior Sparse Generalized Eigenvalue Problems by CG-type Methods on an IBM Regatta Machine
Author
마상백
Keywords
Interior generalized eigenvalue; iterative method; conjugate gradient; preconditioning; parallel; IBM regatta
Issue Date
2007-09
Publisher
한국전산응용수학회
Citation
Journal of Applied Mathematics and Computing, v. 25, No. 1-2, Page. 435-443
Abstract
Computing the interior spectrum of large sparse generalized eigenvalue problems Ax=λBx Ax=λBx , where A and b are large sparse and SPD(Symmetric Positive Definite), is often required in areas such as structural mechanics and quantum chemistry, to name a few. Recently, CG-type methods have been found useful and hence, very amenable to parallel computation for very large problems. Also, as in the case of linear systems proper choice of preconditioning is known to accelerate the rate of convergence. After the smallest eigenpair is found we use the orthogonal deflation technique to find the next m-1 eigenvalues, which is also suitable for parallelization. This offers advantages over Jacobi-Davidson methods with partial shifts, which requires re-computation of preconditioner matrx with new shifts. We consider as preconditioners Incomplete LU(ILU)(0) in two variants, ever-relaxation(SOR), and Point-symmetric SOR(SSOR). We set m to be 5. We conducted our experiments on matrices from discretizations of partial differential equations by finite difference method. The generated matrices has dimensions up to 4 million and total number of processors are 32. MPI(Message Passing Interface) library was used for interprocessor communications. Our results show that in general the Multi-Color ILU(0) gives the best performance.
URI
http://www.koreascience.or.kr/article/JAKO200734516318873.pagehttp://repository.hanyang.ac.kr/handle/20.500.11754/106916
ISSN
1598-5857; 2234-8417
Appears in Collections:
COLLEGE OF COMPUTING[E] > COMPUTER SCIENCE(소프트웨어학부) > Articles
COLLEGE OF COMPUTING[E] > COMPUTER SCIENCE(소프트웨어학부) > Articles
COLLEGE OF COMPUTING[E] > COMPUTER SCIENCE(소프트웨어학부) > Articles
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