Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Journal of Computational and Applied Mathematics
Twostep-by-twostep PIRK-type PC methods with continuous output formulas
Journal of Computational and Applied Mathematics
Software Barrier Performance on Dual Quad-Core Opterons
NAS '08 Proceedings of the 2008 International Conference on Networking, Architecture, and Storage
Parameter optimization for explicit parallel peer two-step methods
Applied Numerical Mathematics
Parallel Low-Storage Runge-Kutta Solvers for ODE Systems with Limited Access Distance
International Journal of High Performance Computing Applications
Scalability and locality of extrapolation methods on large parallel systems
Concurrency and Computation: Practice & Experience
Locality optimized shared-memory implementations of iterated runge-kutta methods
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
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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.