## Contact

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

English title | Rapid solution of boundary value problems on stochastic domains |
---|---|

Applicant | Harbrecht Helmut |

Number | 137669 |

Funding scheme | Project funding (Div. I-III) |

Research institution | Fachbereich Mathematik Departement Mathematik und Informatik Universität Basel |

Institution of higher education | University of Basel - BS |

Main discipline | Mathematics |

Start/End | 01.11.2011 - 30.09.2014 |

Approved amount | 154'699.00 |

uncertainty quantification; boundary value problem; stochastic domain; Karhunen-Loeve expansion

Lead |
---|

Lay summary |

Nowadays, many problems in science and engineering can be numerically solved highly accurate provided that the input data are known exactly. Often, however, the input parameters are not given exactly. The practical significance of highly accurate numerical solution of differential equation models must thus address how to account for uncertain input data. If a statistical description of the input data is available, one can mathematically describe data and solutions as random fields and aim at computation of corresponding deterministic statistics of the unknown random solution. In the present project, we model and compute the solution to problems where the computational domain is uncertain. |

Direct link to Lay Summary | Last update: 21.02.2013 |

Name | Institute |
---|

Name | Institute |
---|

Publication |
---|

On the quasi-Monte Carlo quadrature with Halton points for elliptic PDEs with log-normal diffusion |

Analysis of the domain mapping method for elliptic diffusion problems on random domains |

Combination technique based second moment analysis for elliptic PDEs on random domains |

Multilevel accelerated quadrature for PDEs with log-normally distributed random coefficient. |

Efficient approximation of random fields for numerical applications |

Approximation of bi-variate functions: singular value decomposition versus sparse grids |

Combination technique based k-th moment analysis of elliptic problems with random diffusion |

Comparison of fast boundary element methods on parametric surfaces. |

First order second moment analysis for stochastic interface problems based on low-rank approximation |

Group / person | Country |
---|

Types of collaboration |
---|

Prof. Dr. Reinhold Schneider (TU Berlin) | Germany (Europe) |

- in-depth/constructive exchanges on approaches, methods or results |

Prof. Dr. Christopf Schwab (ETH Zuerich) | Switzerland (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Prof. Dr. Michael Griebel (Uni Bonn) | Germany (Europe) |

- in-depth/constructive exchanges on approaches, methods or results - Publication |

Title | Type of contribution | Title of article or contribution | Date | Place | Persons involved |
---|

27th Chemnitz FEM Symposium | Talk given at a conference | Numerical solution of elliptic diffusion problems on random domains | 22.09.2014 | Chemnitz, Germany | Peters Michael; |

NASPDE 2014 Workshop (Numerical Analysis of Stochastic Partial Differential Equations) | Talk given at a conference | Numerical solution of elliptic diffusion problems on random domains | 09.09.2014 | Lausanne , Switzerland | Harbrecht Helmut; |

Sparse Grids and Applications | Talk given at a conference | Combination technique based k-th moment analysis of elliptic problems with random diffusion | 01.09.2014 | Stuttgart, Germany | Peters Michael; |

SIAM UQ 2014 (SIAM Conference on Uncertainty Quantification) | Talk given at a conference | Multilevel quadrature for elliptic stochastic partial differential equations | 31.01.2014 | Savannah, United States of America | Harbrecht Helmut; |

11th Workshop on fast boundary element methods in industrial applications | Talk given at a conference | H–matrix accelerated second moment analysis for elliptic problems with rough correlation | 26.09.2013 | Hirschegg, Austria | Peters Michael; |

Discrepancy, Numerical Integration and Hyperbolic Cross Approximation | Talk given at a conference | Multilevel quadrature for elliptic stochastic partial differential equations | 23.09.2013 | Bonn, Germany | Harbrecht Helmut; |

ENUMATH 2013 | Talk given at a conference | Multilevel quadrature for elliptic stochastic partial differential equations | 26.08.2013 | Lausanne, Switzerland | Harbrecht Helmut; |

Multiscale and High-Dimensional Problems | Talk given at a conference | Multilevel quadrature for elliptic stochastic partial differential equations | 08.07.2013 | Oberwolfach, Germany | Harbrecht Helmut; |

Mathematisches Kolloquium am Institut fuer Mathematik | Individual talk | Modelling and simulation of elliptic PDEs on random domains | 24.06.2013 | Paderborn, Germany | Harbrecht Helmut; |

Numerical Methods for Uncertainty Quantification | Talk given at a conference | On multilevel quadrature for elliptic stochastic partial differential equations | 13.05.2013 | Bonn, Germany | Harbrecht Helmut; |

SAM Kolloquium an der ETH Zuerich | Individual talk | Modelling and simulation of elliptic PDEs on random domains | 24.04.2013 | Zuerich, Switzerland | Harbrecht Helmut; |

Numerical Methods for PDE Constrained Optimization with Uncertain Data | Talk given at a conference | Modelling and simulation of elliptic PDEs on random domains | 28.01.2013 | Oberwolfach, Germany | Harbrecht Helmut; |

WONAPDE 2013 (Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations) | Talk given at a conference | On multilevel quadrature for elliptic stochastic partial differential equations. | 14.01.2013 | Concepcion, Chile | Harbrecht Helmut; |

IABEM 2013 (Symposium of the International Association for Boundary Element Methods) | Talk given at a conference | Comparison of fast boundary element methods on parametric surfaces | 09.01.2013 | Santiago de Chile, Chile | Harbrecht Helmut; |

10th Workshop on Fast Boundary Element Methods in Industrial Applications | Talk given at a conference | Comparison of Fast Boundary Element Methods on Parametric Surfaces | 27.09.2012 | Hirschegg, Austria | Peters Michael; |

25th Chemnitz FEM-Symposium 2012 | Talk given at a conference | Combination technique based k-th moment analysis of elliptic problems with random diffusion | 24.09.2012 | Chemnitz, Germany | Harbrecht Helmut; |

ESCO 2012 (European Seminar on Computing) | Talk given at a conference | A fast deterministic method for stochastic interface problems | 25.06.2012 | Pilsen, Czech Republic | Harbrecht Helmut; |

Institutsvortrag am Fachbereich fuer Mathematik und Statistik | Individual talk | Gebietsvariationen in Optimierung und Ergebnisverifikation | 08.12.2011 | Konstanz, Germany | Harbrecht Helmut; |

Number | Title | Start | Funding scheme |
---|

169599 | Multilevel Methods and Uncertainty Quantification in Cardiac Electrophysiology | 01.10.2016 | Project funding (Div. I-III) |

156101 | H-matrix based first and second moment analysis | 01.10.2014 | Project funding (Div. I-III) |

We develop an efficient algorithm to compute the Karhunen-Loeve expansion of stochastic fields with nonsmooth covariance kernels. Since the eigenvalues of the covariance operator do not decay exponentially, a large number of eigenpairs need to be approximated. We will employ fast methods for nonlocal operators as for example known from boundary integral equation methods. Then, each eigenpair can be computed in essentially linear complexity.The Karhunen-Loeve expansion is applied to compute the approximate solutions of partial differential equations on stochastic domains. We considerboth, a domain transformation technique and a linearization based on the local shape derivative. Both approaches lead to a boundary value problemon a fixed nominal domain but with stochastic right hand side and/or stochastic coefficients. Stochastic Galerkin and collocation methods will be employed to solve the related boundary value problems.

Swiss National Science Foundation (SNSF)

Wildhainweg 3P.O. Box

CH-3001 Bern

Phone +41 31 308 22 22

Enter and manage your applications

Receive the latest news from us regularly with the SNSF Newsletter.

Continue© SNSF 2021