Probabilistically induced domain decomposition methods for elliptic boundary-value problems

Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few interfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolati...

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Bibliographic Details
Published in:Journal of computational physics Vol. 210; no. 2; pp. 421 - 438
Main Authors: Acebrón, Juan A., Busico, Maria Pia, Lanucara, Piero, Spigler, Renato
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 10.12.2005
Elsevier
Subjects:
Algorithms
Approximation
Boundaries
Boundary value problems
Computational techniques
Computer simulation
Domain decomposition
Exact sciences and technology
Fault-tolerant algorithms
Mathematical analysis
Mathematical methods in physics
Monte Carlo methods
Parallel computing
Physics
Quasi-Monte Carlo methods
Monte Carlo methods
Parallel computing
65C30
Fault-tolerant algorithms
65C05
Quasi-Monte Carlo methods
65N55
Domain decomposition
Helmholtz equations
Domain walls
Decomposition method
Poisson equation
Calculation methods
Algorithms
Boundary-value problems
Calculation
65N55 Monte Carlo methods
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few interfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to split the original problem into fully decoupled subproblems. The numerical treatment can then be continued, implementing any deterministic algorithm on each subdomain. Both, Monte Carlo (or quasi-Monte Carlo) simulations and the domain decomposition strategy allow for exploiting parallel architectures. Scalability and natural fault tolerance are peculiarities of the present algorithm. Examples concern Helmholtz and Poisson equations, whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2005.04.014