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

Dölz, Jürgen and Harbrecht, Helmut and Peters, Michael. (2014) H-matrix accelerated second moment analysis for potentials with rough correlation. Preprints Fachbereich Mathematik, 2014 (03).

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Abstract

We consider the efficient solution of strongly elliptic potential problems with 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)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Dölz, Jürgen and Harbrecht, Helmut and Peters, Michael
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:12 May 2019 22:05
Deposited On:28 Mar 2019 09:52

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