A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs
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State of the art domain decomposition algorithms for large-scale boundary value problems (with M≫ 1 degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers inherent to iterative linear algebra. Here, we introduce PDDSparse, a different approach to scientific supercomputing which relies on a "Feynman-Kac formula for domain decomposition". Concretely, the interfacial values (only) are determined by a stochastic, highly sparse linear system G(ω)u⃗=b⃗(ω) of size O(√(M)), whose coefficients are constructed with Monte Carlo simulations-hence embarrassingly in parallel. In addition to a wider scope for strong scalability in the deep supercomputing regime, PDDSparse has built-in fault tolerance and is ideally suited for GPUs. A proof of concept example with up to 1536 cores is discussed in detail.
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