Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Domain decomposition algorithms with small overlap
SIAM Journal on Scientific Computing
Lower Bounds for Two-Level Additive Schwarz Preconditioners with Small Overlap
SIAM Journal on Scientific Computing
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
Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees
Journal of Computational Physics
Journal of Scientific Computing
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
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A comparison is made between the probabilistic domain decomposition (DD) method and a certain deterministic DD method for solving linear elliptic boundary-value problems. Since in the deterministic approach the CPU time is affected by intercommunications among the processors, it turns out that the probabilistic method performs better, especially when the number of subdomains (hence, of processors) is increased. This fact is clearly illustrated by some examples. The probabilistic DD algorithm has been implemented in an MPI environment, in order to exploit distributed computer architectures. Scalability and fault-tolerance of the probabilistic DD algorithm are emphasized.