Adaptation of a Two-Point Boundary Value Problem Solver to a Vector-Multiprocessor Environment

Systems of linear equations arising from finite-difference discretization of two-point boundary value problems have coefficient matrices that are sparse, with most or all of the nonzeros clustered in blocks near the main diagonal. Some efficiently vectorizable algorithms for factorizing these types of matrices and solving the corresponding linear systems are described. The relative effectiveness of the different algorithms varies according to the distribution of initial, final, and coupled end conditions. The techniques described can be extended to handle linear systems arising from other methods for two-point boundary value problems, such as multiple shooting and collocation. An application to seismic ray tracing is discussed.