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 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 sub-problems. 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 advantage such as scalability obtained increasing the number of processors is shown, both theoretically and experimentally, in a number of test examples, and the possibility of using clusters of computers (grid computing) emphasized.

ACEBRON J., A., BUSICO M., P., Lanucara, P., Spigler, R. (2005). Domain decomposition solution of elliptic boundary-value problems via Monte Carlo and quasi-Monte Carlo methods. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 27, 440-457.

### Domain decomposition solution of elliptic boundary-value problems via Monte Carlo and quasi-Monte Carlo methods

#### Abstract

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 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 sub-problems. 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 advantage such as scalability obtained increasing the number of processors is shown, both theoretically and experimentally, in a number of test examples, and the possibility of using clusters of computers (grid computing) emphasized.
##### Scheda breve Scheda completa Scheda completa (DC)
2005
ACEBRON J., A., BUSICO M., P., Lanucara, P., Spigler, R. (2005). Domain decomposition solution of elliptic boundary-value problems via Monte Carlo and quasi-Monte Carlo methods. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 27, 440-457.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11590/158309`
• ND
• 34
• 31