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
Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees
Journal of Computational Physics
Journal of Scientific Computing
A new domain decomposition approach suited for grid computing
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Scalability and performance analysis of a probabilistic domain decomposition method
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part I
Journal of Computational Physics
A fully scalable parallel algorithm for solving elliptic partial differential equations
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
A stochastic approach to the solution of magnetohydrodynamic equations
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 0.03 |
Domain decomposition of two-dimensional domains on which boundary-value elliptic problems are formulated is accomplished by probabilistic (Monte Carlo) as well as by quasi-Monte Carlo methods, generating only a few interfacial values and interpolating on them. Continuous approximations for the trace of solution are thus obtained, to be used as boundary data for the subproblems. The numerical treatment can then proceed by standard deterministic algorithms, separately in each of the so obtained subdomains. Monte Carlo and quasi-Monte Carlo simulations may naturally exploit multiprocessor architectures, leading to parallel computing, as well as the ensuing domain decomposition does. The advantages such as scalability obtained by increasing the number of processors are shown, both theoretically and experimentally, in a number of test examples, and the possibility of using clusters of computers (grid computing) is emphasized.