Adaptive und parallele Algorithmen zur Lösung partieller
Differentialgleichungen mit variablen Koeffizienten auf dünnen

Third party funded individual grant

Project Details

Project leader:
Prof. Dr. Christoph Pflaum

Project members:
Prof. Dr. Christoph Pflaum

Contributing FAU Organisations:
Professur für Informatik (Numerische Simulation mit Höchstleistungsrechnern)

Funding source: Deutsche Forschungsgemeinschaft (DFG)
Acronym: ParallelSparseGrid
Start date: 29/06/2019
End date: 09/12/2022

Short description (intelligible to all):

Sparse grids are an innovative technique for reducing the computational amount for the numerical solution of partial differential equations. Applications are differential equations on complex domains with reentrant edges and corners or high dimensional problems like the time independent Schrödinger equation. In both cases, accurate numerical solutions are difficult to obtain. In order to apply sparse grids to such differential equations it is important to apply a Ritz-Galerkin discretization.  However, such a discretization leads to several algorithmic difficulties in case of variable coefficients. These difficulties do not appear for a new discretization method on sparse grids, which was recently developed. This discretization applies prewavelets and a discretization with semi-orthogonality. By this concept, PDE's with variable coefficients can efficiently be solved by suitable algorithms. The aim of the project is to continue the development of algorithms for solving PDE's on sparse grids. In particular algorithms on adaptive sparse grids for variable coefficients and efficient algorithms for the calculation of the stiffness matrix have to be developed. Furthermore, new parallelization concepts are needed, since conventional parallelization concepts cannot be applied to sparse grids. The new algorithms will be implemented and analyzed for suitable applications.

Last updated on 2019-28-03 at 09:16