Journal
COMPUTING AND VISUALIZATION IN SCIENCE
Volume 14, Issue 1, Pages 3-15Publisher
SPRINGER
DOI: 10.1007/s00791-011-0160-x
Keywords
Monte Carlo; Multilevel; Stochastic PDE
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Funding
- Engineering and Physical Sciences Research Council under research grants [EP/H051503/1, EP/H051589/1, EP/H05183X/1]
- EPSRC [EP/H051503/1, EP/H05183X/1, EP/H051589/1] Funding Source: UKRI
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We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevelMonte Carlo method, and demonstrate numerically its superiority. The asymptotic cost of solving the stochastic problem with the multilevel method is always significantly lower than that of the standard method and grows only proportionally to the cost of solving the deterministic problem in certain circumstances. Numerical calculations demonstrating the effectiveness of the method for one-and two-dimensional model problems arising in groundwater flow are presented.
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