Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations, blocking communication requests are avoided, which makes it hard to isolate and handle any global vector. While some termination protocols were proposed for asynchronous iterations, only very few of them are based on global residual computation and guarantee effective convergence. But the most effective and efficient existing solutions feature two reduction operations, which constitutes an important factor of termination delay. In this paper, we present new, non-intrusive, protocols to compute a residual error under asynchronous iterations, requiring only one reduction operation. Various communication models show that some heuristics can even be introduced and formally evaluated. Extensive experiments with up to 5,600 processor cores confirm the practical effectiveness and efficiency of our approach.

Summary This paper describes the use of domain decomposition methods for accelerating wave physics simulation. Numerical wave‐based methods provide more accurate simulation than geometrical methods, but at a higher computation cost as well. In the context of virtual reality, the quality of the results is estimated according to human perception, what makes geometrical methods an interesting approach for achieving real‐time physically‐based rendering. Here, we investigate a geometrical method based on both beams and rays tracing, which we enhance by two levels of parallel processing. Techniques from domain decomposition methods are coupled with classical parallel computing on both shared and distributed memory. Both optic and acoustic renderings are experimented to evaluate the acceleration impact of the domain decomposition scheme. Speedup measurements clearly show the efficiency of using domain decomposition methods for real‐time simulation of wave physics. Copyright © 2015 John Wiley & Sons, Ltd.