| Autor: |
Bernal, Francisco, Morón-Vidal, Jorge, Acebrón, Juan A. |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Computers and Mathematics with Applications, 146, 294-308 (2023) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.camwa.2023.07.004 |
| Popis: |
State of the art domain decomposition algorithms for large-scale boundary value problems (with $M\gg 1$ 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 $G(\omega){\vec u}={\vec b}(\omega)$ of size ${\cal O}(\sqrt{M})$, 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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