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2016 ; 374
(2066
): ä Nephropedia Template TP
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English Wikipedia
Some variance reduction methods for numerical stochastic homogenization
#MMPMID27002065
Blanc X
; Le Bris C
; Legoll F
Philos Trans A Math Phys Eng Sci
2016[Apr]; 374
(2066
): ä PMID27002065
show ga
We give an overview of a series of recent studies devoted to variance reduction
techniques for numerical stochastic homogenization. Numerical homogenization
requires that a set of problems is solved at the microscale, the so-called
corrector problems. In a random environment, these problems are stochastic and
therefore need to be repeatedly solved, for several configurations of the medium
considered. An empirical average over all configurations is then performed using
the Monte Carlo approach, so as to approximate the effective coefficients
necessary to determine the macroscopic behaviour. Variance severely affects the
accuracy and the cost of such computations. Variance reduction approaches,
borrowed from other contexts in the engineering sciences, can be useful. Some of
these variance reduction techniques are presented, studied and tested here.