Efficient Parallel Computing of Multifrontal Linear Solver in Block Lanczos Algorithm for Large-Scale Structural Eigenproblems

摘要

A structural eigensolver for large-scale finite element analysis is developed. The algorithms and data structures implemented in this paper are well suited for a distributed memory environment. As an eigenvalue extracting algorithm, the well-known M orthogonal block Lanczos iteration incorporated with a parallel multifrontal solver (PMFS) was chosen. Basically, for the better performance of this algorithm in parallel computation, Lanczos vector allocation, mass matrix multiplication, and M inner product procedures were efficiently implemented. And the PMFS for a linear equation which is the most time-consuming part during Lanczos iterations was improved. The idea was to optimize network topologies of parallel matrix subroutines which are working in a 2-dimensional block-cyclic processor map, as well as to reduce both communication volume and idling time of parallel matrix subroutines. To reduce the communication volume, we condensed the parallel matrix multiplication subroutine from which duplicated communications are observed in the Cholesky factorization phase. To reduce the idling time, we adopted the least common multiple (LCM) concept by inverting a frontal matrix in the triangular system.