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A parallel implementation of a generalized Lanczos procedure for structural dynamic analysis

INTERNATIONAL JOURNAL OF HIGH SPEED COMPUTING 1996年第2期8卷 171-204页

作者： Mackay, DR Law, KH STANFORD UNIV DEPT CIVIL ENGN STANFORD CA 94305 USA

The Lanczos method has rapidly become the preferred method of solution for the generalized eigenvalue problems. The recent emergence of parallel computers has aroused much interest in the practical implementation of the Lanczos algorithm on these high performance computers. This paper describes an implementation of a generalized Lanczos algorithm on a distributed memory parallel computer, with specific application to structural dynamic analysis. One major cost in the parallel implementation of the generalized Lanczos procedure is the factorization of the (shifted) stiffness matrix and the forward and backward solution of triangular systems. In this paper, we review a parallel sparse matrix factorization scheme and propose a strategy for inverting the principal block submatrix factors to facilitate the forward and backward solution of triangular systems on distributed memory parallel computers. We also discuss the different strategies in the implementation of mass-matrix-vector multiplication and how they are used in the implementation of the Lanczos procedure. The Lanczos procedure implemented includes partial and external selective reorthogonalizations. Spectral shifts are introduced when memory space is not sufficient for storing the Lanczos vectors. The tradeoffs between spectral shifts and Lanczos iterations are discussed. Numerical results on Intel's parallel computers, the iPSC/860 hypercube and the Paragon machines will be presented to illustrate the effectiveness and scalability of the parallel generalized Lanczos procedure.

关键词： eigenvalues Lanczos algorithm sparse matrices parallel matrix computation structural dynamics

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