coefficients of divergence
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Author(s):  
Antti Hannukainen ◽  
Jean-Christophe Mourrat ◽  
Harmen T. Stoppels

We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement the method numerically using a finite-element method with hierarchical hybrid grids, which is a semi-implicit method allowing for significant gains in memory usage and execution time. Finally, we demonstrate the efficiency of our approach on two- and three-dimensional examples, for piecewise-constant coefficients with corner discontinuities. For moderate ellipticity contrast and for a precision of a few percentage points, our method allows to compute the homogenized coefficients on a laptop computer in a few seconds, in two dimensions, or in a few minutes, in three dimensions.



1993 ◽  
Vol 2 (1) ◽  
pp. 17-34 ◽  
Author(s):  
Sandra Fortini ◽  
Fabrizio Ruggeri


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