Numerical Solution of PDE's by Sparse Grids

Internally funded project


Project Details

Project leader:
Prof. Dr. Christoph Pflaum

Project members:
Rainer Hartmann

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

Acronym: SparseGrid
Start date: 02/01/2015
End date: 06/12/2019


Research Fields

Lösung partieller Differentialgleichungen mit dünnen Gittern
Professur für Informatik (Numerische Simulation mit Höchstleistungsrechnern)


Abstract (technical / expert description):




  • sparse Grids reduce the computaional amount for solving PDE's





  • efficient algorithms for solving high dimensional  PDE's with variable coefficients on sparse grids





  • solution of high dimensional Schrödinger equation





  • convergence analysis, numerical analysis




Publications

Hartmann, R., & Pflaum, C. (2018). Efficient Ritz-Galerkin Discretization of PDEs with Variable Coefficients in arbitrary Dimensions using Sparse Grids. In PAMM. Weimar: Online: Wiley.
Hartmann, R., & Pflaum, C. (2017). A prewavelet-based algorithm for the solution of second-order elliptic differential equations with variable coefficients on sparse grids. Numerical Algorithms, 1-28. https://dx.doi.org/10.1007/s11075-017-0407-9
Pflaum, C., & Hartmann, R. (2016). A Sparse Grid Discretization of the Helmholtz Equation with Variable Coefficients in High Dimensions. SIAM Journal on Numerical Analysis, 54(4), 2707–2727. https://dx.doi.org/10.1137/15M101508X

Last updated on 2019-22-05 at 14:13