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Bernal, F. & Acebron, J. A. (2016). A multigrid-like algorithm for probabilistic domain decomposition. Computers and Mathematics with Applications. 72 (7), 1790-1810

F. Bernal and J. A. Torres,  "A multigrid-like algorithm for probabilistic domain decomposition", in Computers and Mathematics with Applications, vol. 72, no. 7, pp. 1790-1810, 2016

@article{bernal2016_1714832652758,
	author = "Bernal, F. and Acebron, J. A.",
	title = "A multigrid-like algorithm for probabilistic domain decomposition",
	journal = "Computers and Mathematics with Applications",
	year = "2016",
	volume = "72",
	number = "7",
	doi = "10.1016/j.camwa.2016.07.030",
	pages = "1790-1810",
	url = "http://www.sciencedirect.com/science/article/pii/S0898122116304357"
}

TY  - JOUR
TI  - A multigrid-like algorithm for probabilistic domain decomposition
T2  - Computers and Mathematics with Applications
VL  - 72
IS  - 7
AU  - Bernal, F.
AU  - Acebron, J. A.
PY  - 2016
SP  - 1790-1810
SN  - 0898-1221
DO  - 10.1016/j.camwa.2016.07.030
UR  - http://www.sciencedirect.com/science/article/pii/S0898122116304357
AB  - We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control variates in order to reduce the Monte Carlo error of the following iterates-resulting in an overall acceleration of PDD for a given error tolerance. The key feature of the proposed algorithm is the ability to approximately predict the speedup with little computational overhead and in parallel. Besides, the theoretical framework allows to explore other aspects of PDD, such as stability. One numerical example is worked out, yielding an improvement between one and two orders of magnitude over the previous version of PDD.
ER  -