FWF Project P21732
Adaptive Boundary Element Method
Address:
Prof. Dr. Dirk Praetorius
Institute for Analysis and Scientific Computing (Inst. E 101)
Vienna University of Technology
Wiedner Hauptstraße 8-10
1040 Wien, Austria
Contact:
| FON FAX WWW |
++43 1 58801-10150 ++43 1 58801-10196 dirk.praetorius@tuwien.ac.at http://www.asc.tuwien.ac.at/abem |
Aims:
For two reasons, fast and accurate error estimation plays a key role in reliable and efficient scientific computing: First, one may want to check whether the solution of a numerical simulation is accurate enough. Second, if this is not the case, one aims to improve the discretization, e.g., by local refinement of the underlying mesh.
Both subjects are usually covered by so-called a posteriori error estimates and related adaptive mesh-refining algorithms. For error control in finite element methods (FEM), there is a broad variety of a posteriori error estimators available, and convergence as well as optimality of adaptive algorithms is well studied in the literature. This is in sharp contrast to the boundary element method (BEM), where only few a posteriori error estimators have been proposed. Moreover, even convergence of adaptive BEM is widely open. Finally, unlike the FEM, most a posteriori error estimators for BEM are computationally expensive and even implementationally challenging.
The aim of the project is therefore threefold: First, to give a fair numerical comparison between the error estimators and adaptive mesh-refining algorithms proposed in the BEM literature. Second, to develop a posteriori error estimators in the context of BEM which are numerically cheap to compute. Third, to study the convergence and the optimality of associated adaptive algorithms.
Funding Period:
FWF grant from 08/2009 until 07/2012
Research Activities:
| 01/2013 | Participation and contribution (2 talks) to WONAPDE 2013 Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Conception/Chile |
| 01/2013 | Participation and contribution (3 talks) to IABEM 2013 Symposium of the International Association for Boundary Element Methods, Santiago/Chile |
| 11/2012 | Dr Michael Karkulik gave a talk on the results of his PhD thesis at the Institute of Numerical Mathematics of TU Graz |
| 10/2012 | Dr Michael Karkulik successfully defended his PhD thesis on Convergence and quasi-optimality of adaptive BEM (with distinction). Congratulations! |
| 10/2012 | Participation and contribution (4 talks) to 10th Workshop on Fast Boundary Element Methods in Industrial Applications in Hirschegg/Austria |
| 09/2012 | Participation and contribution (3 talks) to 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) in Vienna/Austria |
| 09/2012 | Participation and contribution (1 talk) to Algoritmy 2012 Conference in Podbanske/Slowakia |
| 08/2012 | Participation and contribution (1 talk) to 7th Zürich Summerschool on A Posteriori Error Control and Adaptivity in Zürich/Switzerland |
| 07/2012 | Participation and contribution (2 talks) to Computational Methods in Applied Mathematics CMAM-5 in Berlin/Germany |
| 05/2012 | Participation and contribution (2 talks) to 8th Austrian Numerical Analysis Day in Vienna/Austria |
| 05/2012 | Participation and contribution (2 talks) to BEM on the Saar 2012 in Saarbrücken/Germany |
| 05/2012 | Participation and contribution (1 talk) to BEM @ Deich Workshop on the occasion of Prof Ernst Stephan's 65th birthday in Cappel Neufeld/Germany |
| 04/2012 | Research visit at Humboldt University of Berlin/Germany for cooperation with Prof Carsten Carstensen |
| 03/2012 | Dipl.-Ing. Michael Feischl has successfully finished his master thesis on Optimality of adaptive 2D boundary element method (with distinction). Congratulations! |
| 02/2012 | Participation and contribution (1 poster, 1 talk) to Workshop on Trends in Computational Science and Engineering at TU Wien |
| 02/2012 | Michael Ebner, BSc has successfully finished his bachelor thesis on A posteriori error estimation for Symm's integral equation. Congratulations! |
| 12/2011 | Participation and contribution (1 talk) to WPI Workshop on Efficient mesh adaptation methods for evolution problems: theory and applications at Wolfang-Pauli-Institute, Wien |
| 12/2011 | Josef Kemetmüller, BSc has successfully finished his bachelor thesis on Vectorized implementation of P1-FEM in 3D. Congratulations! |
| 12/2011 | Research stay of Prof Ernst Stephan (U Hanover) at TU Wien |
| 11/2011 | Research visit at Leibniz-University of Hanover/Germany for cooperation with Prof Ernst Stephan |
| 10/2011 | Participation and contribution (3 talks) to 9th Workshop on Fast Boundary Element Methods in Industrial Applications in Hirschegg/Austria |
| 10/2011 | Dr Markus Aurada has successfully defended his PhD thesis on Mixed conforming elements for the large-body limit in micromagnetics (with distinction). Congratulations! |
| 09/2011 | Participation and contribution (2 talks) to IABEM Conference 2011 of International Association for Boundary Element Methods in Brescia/Italy |
| 07/2011 | David Pavlicek, BSc has successfully finished his bachelor thesis on Optimality of adaptive FEM. Congratulations! |
| 05/2011 | Participation and contribution (1 talk) to 7th Austrian Numerical Analysis Day in Graz/Austria |
| 04/2011 | Participation and contribution (2 talks) to Annual GAMM Meeting 2011 in Graz/Austria |
| 02/2011 | Dr Samuel Ferraz-Leite has successfully defended his PhD thesis on Quadratic minimization with non-local operators and non-linear constraints (with distinction). Congratulations! |
| 01/2011 | Participation and contribution (1 talk) to 2nd African Conference on Computational Mechanics in Cape Town/South Africa |
| 10/2010 | Participation and contribution (2 talks) to 8th Workshop on Fast Boundary Element Methods in Industrial Applications in Hirschegg/Austria |
| 07/2010 | Invited talk at Max-Planck-Institute for Mathematics in the Sciences in Leipzig/Germany |
| 07/2010 | Release 2.0 of Matlab BEM library HILBERT |
| 06/2010 | Research stay of Dr Matthias Maischak (Brunel University, Uxbridge/UK) at TU Wien |
| 06/2010 | HILBERT meeting with work group of Prof Stefan Funken (U Ulm) at Söllerhaus/Austria |
| 06/2010 | Research stay of Dr Günther Of (Graz University of Technology, AT) at TU Wien |
| 05/2010 | Marcus Page, MSc has successfully finished his master thesis on Estimator reduction principle and convergence of adaptive FEM for obstacle problems (with distinction). Congratulations! |
| 05/2010 | Participation and contribution (2 talks) to 6th Austrian Numerical Analysis Day in Salzburg/Austria |
| 03/2010 | Markus Mayr, BSc has successfully finished his bachelor thesis on Stable implementation of boundary element method on strongly adapted meshes. Congratulations! |
| 02/2010 | Michael Feischl, BSc has successfully finished his bachelor thesis on Different strategies for the adaptive FEM-BEM coupling. Congratulations! |
| 01/2010 | Research stay of work group of Prof Stefan Funken (U Ulm) at TU Wien |
| 01/2010 | Participation and contribution (1 talk) to WONAPDE 2010 - Third Chilean Workshop on Numerical Analysis of Partial Differential Equations in Concepcion/Chile |
| 11/2009 | Release 1.0 of Matlab BEM library HILBERT |
| 10/2009 | Participation and contribution (3 talks) to 7th Workshop on Fast Boundary Element Methods in Industrial Applications in Hirschegg/Austria |
| 09/2009 | Participation and contribution (2 talks) to 17th ÖMG Congress / Annual DMV Conference in Graz/Austria |
| 09/2009 | Kick-off workshop on BEM with work group of Prof Stefan Funken (U Ulm) in Cortona/Italy |
| since 08/2009 | Development of Matlab software HILBERT for adaptive lowest-order BEM |