Invariant imbedding and the method of lines for parallel computers (Q1124295)

The imbedding method allows the solution of a linear two-point boundary value problem to be expressed in terms of the solution of initial value problems. They can be solved independently over subintervals of the given interval and then combined using stable recursion. This ability to compute in parallel over subintervals makes invariant imbedding an attractive method for parallel computation. The parallel implementation of invariant imbedding can be used in conjunction with the method of lines to solve partial differential equations. The problem of assigning lines to processors to minimize communication delays and the effect of asynchronous relaxation are considered. Each algorithm is implemented and run on the NCUBE/ten hypercube, and timing data, speedup and normalized speedup are given. Operation counts are also given for each algorithm.