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GPU accelerated Monte Carlo sampling for SPDEs

: Shegunov, N.; Armianov, P.; Semerdjiev, A.; Iliev, O.

Fulltext ()

Dimitrov, V.:
ISGT 2018 Information Systems and Grid Technologies. Online resource : Proceedings of the Information Systems and Grid Technologies, Sofia, Bulgaria, November 16-17, 2018
La Clusaz: CEUR, 2019 (CEUR Workshop Proceedings 2464)
ISSN: 1613-0073
International Conference "Information Systems and Grid Technologies" (ISGT) <12, 2018, Sofia>
Conference Paper, Electronic Publication
Fraunhofer ITWM ()

Monte Carlo sampling methods is a broad class of computational
algorithms, that rely on repeated random sampling to obtain numerical
results. The idea of such algorithms is to introduce randomness
to solve problems, even in the deterministic case. Such algorithms
are often used in physical and mathematical problems and are most
useful when it is difficult or impossible to use other approaches due to
limitations, such as cost of performing experiment or inability to take
direct measures. The problems typically require solving a stochastic
partial differential equations (SDPEs), where an uncertainty is incorporated
in to the model. For example: as an input parameter, or
initial boundary condition. Extensive efforts have been devoted to
the development of accurate numerical algorithms, so that simulation
predictions are reliable in since that the numerical errors are well understood
and under control for practical problems. Multilevel Monte
Carlo (MLMC) is a novel idea. Instead of sampling from the true solution,
a sampling is done at different levels. Such approach is beneficial
in terms of convergence rate. However for practical simulations a large
number of problems has to be solved, with huge number of unknowns.
Such computational restrictions naturally leads to challenging parallel
algorithms. To overcome some of the limitations, here we consider a
parallel implementation of MLMC algorithm for a model SPDE, that
uses GPU acceleration for the permeability generation.