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H-matrix based second moment analysis for rough random fields and finite element discretizations

Dölz, Jürgen and Harbrecht, Helmut and Peters, Michael. (2015) H-matrix based second moment analysis for rough random fields and finite element discretizations. Preprints Fachbereich Mathematik, 2015 (35).

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Abstract

We consider the efficient solution of strongly elliptic partial differential equations with random load based on the finite element method. The solution's two-point correlation can efficiently be approximated by means of an H-matrix, in particular if the correlation length is rather short or the correlation kernel is non-smooth. Since the inverses of the finite element matrices which correspond to the differential operator under consideration can likewise efficiently be approximated in the H-matrix format, we can solve the correspondent H-matrix equation in essentially linear time by using the H-matrix arithmetic. Numerical experiments for three dimensional finite element discretizations for several correlation lengths and different smoothness are provided. They validate the presented method and demonstrate that the computation times do not increase for non-smooth or shortly correlated data.
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:07 May 2019 16:01
Deposited On:28 Mar 2019 09:51

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