A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs Articles uri icon

publication date

  • July 2023

start page

  • 294

end page

  • 308


  • 146

International Standard Serial Number (ISSN)

  • 0898-1221

Electronic International Standard Serial Number (EISSN)

  • 1873-7668


  • 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.


  • Mathematics


  • high-performance computing (hpc); scientific computing; domain decomposition; strong scalability; probabilistic domain decomposition; feynman-kac