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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
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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
  • AN ASSESSMENT OF PARALLEL PRECONDITIONERS FOR THE INTERIOR SPARSE GENERALIZED EIGENVALUE PROBLEMS BY CG-TYPE METHODS ON AN IBM REGATTA MACHINE
저자명
Ma. Sang-Back,Jang. Ho-Jong
간행물명
Journal of applied mathematics & computing
권/호정보
2007년|25권 1호|pp.435-443 (9 pages)
발행정보
한국전산응용수학회
파일정보
정기간행물|ENG|
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이 논문은 한국과학기술정보연구원과 논문 연계를 통해 무료로 제공되는 원문입니다.
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기타언어초록

Computing the interior spectrum of large sparse generalized eigenvalue problems $Ax;=;{lambda}Bx$, 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.