Mathematics Colloquium

Ralf Hiptmair

(ETH Zürich)

"Sparse adaptive finite elements for radiative transfer"

Date: Mon, September 6, 2010
Time: 17:15
Place: Research II Lecture Hall

Abstract: We propose an adaptive multilevel Galerkin FEM for the numerical solution of the linear radiative transfer equation. Our approach is based

An a-priori error analysis shows, under strong regularity assumptions on the solution, that the sparse tensor product method is clearly superior to a discrete ordinates method, as it converges with essentially optimal asymptotic rates while its complexity grows essentially only as that for a linear transport problem in Rn. Numerical experiments for n=2 on a set of example problems agree with the convergence and complexity analysis of the method and show that introducing adaptivity can improve performance in terms of accuracy vs. number of degrees even further.