Optimized extrapolation methods for parallel solution of IVPs on different computer architectures

Abstract

Extrapolation methods are known to be well suited for parallelism, but parallel execution of codes optimized for sequential computation cannot be optimal on parallel machines. Here we present parallel implementations on different architectures of the two most widely used extrapolation methods: The extrapolated mid-point rule for nonstiff systems and the extrapolated semi-implicit Euler method for stiff systems. The architectures include shared memory, distributed and virtually shared memory systems, and the number of processors can be fixed, unlimited, or dynamically limited throughout runtime. A speedup of more than a factor 3 is possible if the algorithms are optimized for the according architectures.