A fully scalable algorithm suited for petascale computing and beyond

Nowadays supercomputers have already entered in the petascale computing era and peak rate performance is dramatically increasing year after year. However, most of current algorithms are not capable of exploiting fully such a technology due to the well-known parallel programming related issues, such as synchronization, communication and fault tolerance. The aim of this paper is to present a probabilistic domain decomposition algorithm based on generating suitable random trees for solving nonlinear parabolic partial differential equations. These are of paramount importance since many important scientific and engineering problems are modeled by such type of differential equations. We stress that such algorithm is perfectly suited for both current and future high performance supercomputers, showing a remarkable performance and arbitrary scalability.While classical algorithms based on a deterministic domain decomposition exhibits strong limitations when increasing the size of the problem and the number of processors involved, probabilistic methods rather allow us to exploit efficiently massively parallel architectures, being the problem fully decoupled. Large-scale simulations runned on a high performance supercomputer confirm such properties.

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