• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.435-443
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• 2007

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.

• 지식정보인프라
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• 통권6호
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• pp.140-147
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• 2001

전체가 벡터형 단일 기종이었던 이전의 두 시스템과는 달리 슈퍼컴퓨터 3호기의 경우는 시스템 전체 규모의 대부분을 범용 RISC프로세서를 사용하는 IBM Regatta 시스템이 차지하고 있고 벡터형 시스템인 NEC SX-5의 규모는 상대적으로 매우 작은 편이다. 따라서 본고에서는 이러한 형태의 시스템 도입이 결정된 과정과 그런 결론을 내게 만든 슈퍼컴퓨팅 환경의 변화와 슈퍼컴퓨팅 기술의 동향에 대해 살표보고 나아가서 앞으로의 변화 추세를 도입이 결정된 시스템을 중심으로 살펴보고자 한다.