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Adams---Bashforth methods are a well-known class of explicit linear multi-step methods for the solution of initial value problems of ordinary differential equations. This article discusses different data-parallel implementation variants with different loop structures and communication patterns and compares the resulting locality and scalability. In particular, pipelining of time steps is employed to improve the locality of memory references. The comparison is based on detailed runtime experiments performed on parallel computer systems with different architectures, including the two supercomputer systems JUROPA and HLRB II.

Locality Improvement of Data-Parallel Adams–Bashforth Methods through Block-Based Pipelining of Time Steps