des DFG-Sonderforschungsbereichs 393

Numerische Simulation auf massiv parallelen Rechnern

Zeit: Freitag, 25.4.2003, 11:00 Uhr
Ort: Reichenhainer Straße 70, B 202
Vortragender: Stefan Achatz (TU München)
Thema: Adaptive higher order finite elements over sparse grids for partial differential equations with variable coefficients

Function spaces over sparse grids lead to an O(N^{-p}) approximation with respect to the H_0^1-Norm, where standard finite elements usually give O(N^{-p/d}) (N number of degrees of freedom, p polynomial degree of trial functions, d dimension). Unfortunately, due to the tensor product construction of sparse grids and due to the algorithms used so far, the sparse grid FEM (in its pure version) is restricted to partial differential equations with constant coefficients over rectangular domains.

In this talk I will present a simple approach, how to adapt the sparse grid FEM to rather general elliptic problems on smoothly bounded domains by modifying the stiffness matrix in an appropriate way. Consistency and stability of the resulting method will be discussed. By means of some numerical examples the method's quality is shown and compared to standard finite elements. If there is time, I shall give an overview on the multilevel preconditioner I implemented in order to solve the problems efficiently.

Das Seminar wird von Prof. Meyer geleitet. Interessenten sind herzlich eingeladen.

Gerd Kunert,