A Parallel Implementation of a Generalized Lanczos Procedure for Structural Dynamic Analysis

This paper describes a parallel implementation of a generalized Lanczos procedure for struc-tural dynamic analysis on a distributed memory parallel computer. One major cost of the gener-alized Lanczos procedure is the factorization of the (shifted) stiffness matrix and the forward and backward solution of triangular systems. In this paper, we discuss load assignment of a sparse matrix and propose a strategy for inverting the principal block submatrix factors to facilitate the forward and backward solution of triangular systems. We also discuss the different strategies in the implementation of mass matrix-vector multiplication on parallel computer and how they are used in the Lanczos procedure. The Lanczos procedure implemented includes partial and external selective reorthogonalizations and spectral shifts. Experimental results are presented to illustrate the effectiveness of the parallel generalized Lanczos procedure. The issues of balancing the com-putations among the basic steps of the Lanczos procedure on distributed memory computers ar