Solution methods for static and dynamic structural analysis on distributed memory computers

Increasingly large and complex finite element problems require the computational power of parallel computers. This thesis studies solution methods for static and dynamic structural finite element analysis on a distributed memory parallel computer.; Sparse matrix methods seek to exploit the large number of zero entries by eliminating the storage and computation of the zero entries in the matrix factor. A row oriented sparse matrix factorization scheme is developed to solve the typically sparse, symmetric, and positive definite global stiffness matrix resulting from finite element structural analysis. This scheme is rich in vector dot products which is important to optimize performance on RISC processors. Results are presented from its implementation on both a workstation and a distributed memory parallel computer, the Intel iPSC/i860 hypercube.; In general, the forward and backward solution of triangular systems do not parallelize well due to the small amount of work involved in the solution of a triangular system and to the sequential nature of forward and backward substitution. In this work, we show that dense subblocks of the matrix factor can be inverted without any extra communication costs between processors, or increasing the fills in the sparse matrix factor. This partial matrix factor inversion significantly reduces the amount of time required for a forward and backward solution on a distributed memory parallel computer. This is particularly important for problems with more than one right hand side vectors.; The analysis of natural frequencies and modes of vibration in structural dynamics is often posed as a generalized eigenproblem. Lanczos algorithm has become the preferred method to solve the resulting generalized eigenvalue problem in finite element structural dynamics. A parallel Lanczos algorithm is implemented on the Intel iPSC/i860 hypercube. This algorithm includes a spectral shift to improve the convergence and relies on partial and external selective reorthogonalization. The partial matrix factor inverse is also included in the implementation of Lanczos algorithm. The vector solution phase is shown to dominate the time required to solve for the eigenvalues and associated eigenvectors using Lanczos algorithm.