BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-92-09
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: An implementation of a generalized Lanczos procedure for
               structural dynamic analysis on distributed memory computers
        TYPE:: Manuscript
      AUTHOR:: Mackay, David R.
      AUTHOR:: Law, Kincho H.
        DATE:: August 1992
       PAGES:: 52
    ABSTRACT:: This paper describes a parallel implementation of a
               generalized Lanczos procedure for structural dynamic analysis
               on a distributed memory parallel computer. One major cost 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 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 computers
               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 computations among the basic steps of the
               Lanczos procedure on distributed memory computers are
               discussed.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-92-09