Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Sunday, January 26th, 1997

On the correct and reliable resolution of different scales in finite element analysis of exterior Helmholtz problems

Exterior problems for time-harmonic wave propagation are inherently multiscalar. Firstly, the numerical method has to resolve the finite scale of the source/obstacle as well as the infinite scale of the exterior region. In particular, it is important that the far field behavior of the exact model it represented correctly in the approximate model. Secondly, the length of the radiated or incident/scattered waves may be small compared to the size of the source/obstacle. The relation small wavelength/large scattering object leads to Helmholtz equations with large (non-dimensional) wavenumber. It can be shown that the stability of the numerical model deteriorates with the size of the wavenumber. This has an important effect on the accuracy and reliability of the numerical model. In our talk, we address both aspects of the problem. Refering to the incorporation of the infinite scale, we present new results from a convergence analysis of a coupled FEM-infinite element method (with L. Demkowicz). Regarding the resolution of small wavelengthes, we give results from our analysis of the h-p-method of the FEM (with I. Babuska).