BESTHEA
Space-time boundary element methods for the heat equation
Project overview
BESTHEA is the joint Austrian-Czech project Space-Time Boundary Element Methods for the Heat Equation supported by the Austrian Science Fund (FWF) and the Czech Science Foundation (GAČR). The aim of the project is to develop fast highly scalable parallel solver for the heat equation in 3D based on the space-time boundary element method which will enable adaptive refinement in space and time. The jointly developed software is called BESTHEA (Boundary Element Solver for The Heat EquAtion) as well.
Partners
The Institute of Applied Mathematics at the Graz University of Technology focuses on numerical analysis and research of finite and boundary element methods as well as domain decomposition methods.
IT4Innovations at VŠB-TU Ostrava provides supercomputing services mainly to Czech science community but focuses also on its own scientific code development.
Team members
Günther Of (PI) is an Associate Professor at the Institute of Applied Mathematics, Graz University of Technology. He focuses on numerical analalysis, fast boundary element methods, and domain decomposition methods.
Michal Merta (PI) is a Researcher at IT4Innovations, VŠB-TU Ostrava. His research interests include parallel computing or boundary element method.
Jan Zapletal is a Senior Researcher at IT4Innovations. He focuses on boundary element methods and parallel computing.
Michal Kravcenko is a Research Assistant and PhD. student at IT4Innovations. His research interests include parallel computing or graph theory.
Raphael Watschinger is a Research Assistant and PhD student at the Institute of Applied Mathematics, Graz University of Technology. His research interests include fast boundary element methods for the Helmholtz and the heat equation.
Software repository
A public software repository with the BESTHEA library is available at https://github.com/zap150/besthea.
Publications
Watschinger, R., Merta, M., Of, G., Zapletal, J. A parallel fast multipole method for a space-time boundary element method for the heat equation. Under review (2021). arXiv:2106.15911.
Watschinger, R., Of, G. An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions. Uder review (2021). arXiv:2104.15024.
Zapletal, J., Watschinger, R., Of, G., Merta, M. Semi-analytic integration for a parallel space-time boundary element method modeling the heat equation. Under review (2021). Preprint: arXiv:2102.09811.
Dohr, S., Zapletal, J., Of, G., Merta, M., Kravcenko, M. A parallel space-time boundary element method for the heat equation. Computers & Mathematics with Applications, 2019. DOI: https://doi.org/10.1016/j.camwa.2018.12.031.
Presentations & Posters
2020_10_soellerhaus-2.pdfOf, Merta, Watschinger, Zapletal. Implementation of boundary element integration schemes for the heat equation in 3D. 18. Soellerhaus Workshop, 2020, Hirschegg, Austria.
Soellerhaus19.pdfWatschinger, Of. A causal FMM for a space-time BEM for the heat equation with non-uniform time steps. 17. Soellerhaus Workshop, 2019, Hirschegg, Austria.
2019_05_hpcse_of.pdfDohr, Kravcenko, Merta, Of, Steinbach, Zapletal. A parallel space-time boundary element method for the heat equation. HPCSE 2019, Soláň, Czech Republic.
2018_06_esco.pdfDohr, Merta, Of, Zapletal. Efficient evaluation of space-time boundary integral operators on SIMD architectures. ESCO 2018, Pilsen, Czech Republic
2019_05_HPCSE_Solan.pdfMerta, Zapletal, Of, Dohr. A parallel space-time boundary element method for the heat equation. HPCSE 2019, Soláň, Czech Republic.
Contact
Günther Of
Technische Universität Graz
Institut für Angewandte Mathematik
Steyrergasse 30
A 8010 Graz
of <at> tugraz.at
Michal Merta
VŠB-Technická univerzita Ostrava
IT4Innovations
17. listopadu 2172/15
708 00 Ostrava
michal.merta <at> vsb.cz