Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Exponential Timestepping with Boundary Test for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Fast simulations of stochastic dynamical systems
Journal of Computational Physics
SIAM Journal on Scientific Computing
Probabilistically induced domain decomposition methods for elliptic boundary-value problems
Journal of Computational Physics
Supercomputing applications to the numerical modeling of industrial and applied mathematics problems
The Journal of Supercomputing
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In this paper, we analyze the scalability and performance of a probabilistic domain decomposition strategy for solving linear elliptic boundary-value problems. Such a strategy consists of a hybrid numerical scheme based on a probabilistic method along with a domain decomposition, and full decoupling can be accomplished. It is shown that such a method performs well for an arbitrarily large number of processors, while the classical deterministic approach is strongly affected by intercommunications. Therefore, the overall performance degrades dramatically for rather large number of processors. Furthermore, we find that the probabilistic method is scalable as the number of subdomains, i.e., the number of processors involved, increases. This fact is clearly illustrated by an example.