Data Entry: Please note that the research database will be replaced by UNIverse by the end of October 2023. Please enter your data into the system https://universe-intern.unibas.ch. Thanks

Login for users with Unibas email account...

Login for registered users without Unibas email account...

 
H-matrix based first and second moment analysis
Third-party funded project
Project title H-matrix based first and second moment analysis
Principal Investigator(s) Harbrecht, Helmut
Project Members Dölz, Jürgen
Organisation / Research unit Departement Mathematik und Informatik / Computational Mathematics (Harbrecht)
Project start 01.10.2014
Probable end 20.09.2017
Status Completed
Abstract

We compute the expectation and the two-point correlation of the solution to partial differential equations with roughly correlated random input parameters. Besides random loadings, by a shape Taylor expansion, we particularly treat random domains. The two-point correlation satisfies a boundary value problem on the product domain which involves the tensor product of the differential or pseudo-differential operator under consideration. The computation of the solution’s two-point correlation is well understood if the two-point correlation of the given correlation kernel is sufficiently smooth. Unfortunately, the problem becomes much more involved in case of rough data. We will apply the concept of the H-matrix arithmetic to get a powerful tool to cope with this problem. By employing a parametric domain or 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.

We compute the expectation and the two-point correlation of the solution to partial differential equations with roughly correlated random input parameters. Besides random loadings, by a shape Taylor expansion, we particularly treat random domains. The two-point correlation satisfies a boundary value problem on the product domain which involves the tensor product of the differential or pseudo-differential operator under consideration. The computation of the solution’s two-point correlation is well understood if the two-point correlation of the given correlation kernel is sufficiently smooth. Unfortunately, the problem becomes much more involved in case of rough data. We will apply the concept of the H-matrix arithmetic to get a powerful tool to cope with this problem. By employing a parametric domain or 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.

Keywords H-matrix arithmetic, perturbation method, roughly correlated random fields, partial differential equations on random domains
Financed by Swiss National Science Foundation (SNSF)

Published results ()

  ID Autor(en) Titel ISSN / ISBN Erschienen in Art der Publikation
3660289  Dölz, Jürgen; Harbrecht, Helmut; Peters, Michael  An interpolation-based fast multipole method for higher order boundary elements on parametric surfaces  0029-5981 ; 1097-0207  International Journal for Numerical Methods in Engineering  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
3697040  Dambrine, Marc; Greff, Isabelle; Harbrecht, Helmut; Puig, Benedicte  Numerical solution of the homogeneous Neumann boundary value problem on domains with a thin layer of random thickness  0021-9991  Journal of Computational Physics  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
3766604  Dölz, Jürgen; Harbrecht, Helmut; Schwab, Christoph  Covariance regularity and H-matrix approximation for rough random fields  0029-599X  Numerische Mathematik  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
3232640  Doelz, J.; Harbrecht, H.; Peters, M.  H-matrix accelerated second moment analysis for potentials with rough correlation  0885-7474  Journal of scientific computing  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
4093439  Dölz, Jürgen; Harbrecht, Helmut; Kurz, Stefan; Schöps, Sebastian; Wolf, Felix  A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems  0045-7825  Computer Methods in Applied Mechanics and Engineering  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
3886588  Dölz, Jürgen; Harbrecht, Helmut; Peters, Michael  H-matrix based second moment analysis for rough random fields and finite element discretizations  1064-8275 ; 1095-7197  SIAM Journal on Scientific Computing  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
4152010  Dölz, Jürgen  Hierarchical Matrix Techniques for Partial Differential Equations with Random Input Data      Publication: Thesis (Dissertationen, Habilitationen) 
4480772  Dölz, Jürgen; Harbrecht, Helmut  Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains  0021-9991 ; 1090-2716  Journal of Computational Physics  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
4497697  Harbrecht, Helmut; Dölz, Jürgen; Multerer, Michael D.  On the Best Approximation of the Hierarchical Matrix Product  0895-4798 ; 1095-7162  SIAM journal on matrix analysis and applications  Publication: JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift) 
   

MCSS v5.8 PRO. 0.421 sec, queries - 0.000 sec ©Universität Basel  |  Impressum   |    
28/03/2024