تقرير
A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs
| العنوان: | A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs |
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| المؤلفون: | Bernal, Francisco, Morón-Vidal, Jorge, Acebrón, Juan A. |
| المصدر: | Computers and Mathematics with Applications, 146, 294-308 (2023) |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.camwa.2023.07.004 |
| الوصول الحر: | http://arxiv.org/abs/2301.05780Test |
| رقم الانضمام: | edsarx.2301.05780 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.camwa.2023.07.004 |
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