A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs
Articles
Overview
published in
publication date
- July 2023
start page
- 294
end page
- 308
volume
- 146
Digital Object Identifier (DOI)
full text
International Standard Serial Number (ISSN)
- 0898-1221
Electronic International Standard Serial Number (EISSN)
- 1873-7668
abstract
- State of the art domain decomposition algorithms for large-scale boundary value problems (with 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 of size, 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.
Classification
subjects
- Mathematics
keywords
- high-performance computing (hpc); scientific computing; domain decomposition; strong scalability; probabilistic domain decomposition; feynman-kac