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Error estimation and adaptive computation forelliptic problems with randomly perturbed coefficients
Axel Malqvist
UCSD Department of Mathematics
Abstract:
We develop and analyze an efficient numerical method for computingthe response of the solution of an elliptic problem with randomlyperturbed coefficients. We use a variational analysis based on the adjointoperator to deal with the perturbations in data. To deal withperturbations in the diffusion coefficient, we construct a piecewiseconstant approximation to the random perturbation then use domaindecomposition to decompose the problem into sub-problems on whichthe diffusion coefficient is constant. To compute local solutions ofthe sub-problems, we use the infinite series for the inverse of aperturbation of an invertible matrix to devise a fast way to computethe effects of variation in the parameter. Finally, we derive aposteriori error estimates that take into account all the sourcesof error and derive a new adaptive algorithm that provides aquantitative way to distribute computational resources between allof the sources.
Tuesday, November 7, 2006
11:00AM AP&M 2402
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Randolph E. Bank
Philip E. Gill
Michael Holst
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Axel Malqvist
UCSD Department of Mathematics
Abstract:
We develop and analyze an efficient numerical method for computingthe response of the solution of an elliptic problem with randomlyperturbed coefficients. We use a variational analysis based on the adjointoperator to deal with the perturbations in data. To deal withperturbations in the diffusion coefficient, we construct a piecewiseconstant approximation to the random perturbation then use domaindecomposition to decompose the problem into sub-problems on whichthe diffusion coefficient is constant. To compute local solutions ofthe sub-problems, we use the infinite series for the inverse of aperturbation of an invertible matrix to devise a fast way to computethe effects of variation in the parameter. Finally, we derive aposteriori error estimates that take into account all the sourcesof error and derive a new adaptive algorithm that provides aquantitative way to distribute computational resources between allof the sources.
Tuesday, November 7, 2006
11:00AM AP&M 2402