H-matrix accelerated second moment analysis for potentials with rough correlation

Dölz, Jürgen and Harbrecht, Helmut and Peters, Michael. (2015) H-matrix accelerated second moment analysis for potentials with rough correlation. Journal of scientific computing, Vol. 65, H. 1. pp. 387-410.

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Official URL: http://edoc.unibas.ch/dok/A6438727

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We consider the efficient solution of partial differential equationsfor strongly elliptic operators with constant coefficients and stochastic Dirichlet data by the boundary integral equation method. The computation of the solution's two-point correlation is well understood if the two-point correlation of the Dirichlet data is known and sufficiently smooth.Unfortunately, the problem becomes much more involved in case of rough data. We will show that the concept of the H-matrix arithmetic provides a powerful tool to cope with this problem. By employing a parametric surface representation, we end up with an H-matrix arithmetic based on balanced cluster trees. This considerably simplifies the implementation and improves the performance of the H-matrix arithmetic. Numerical experiments are provided to validate and quantify the presented methods and algorithms.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Dölz, Jürgen and Peters, Michael
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:31 Dec 2015 10:58
Deposited On:06 Nov 2015 10:21

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