Universität Augsburg

Professor Dr. Euan Spence
University of Bath
spricht am
Dienstag, 14. Januar 2020
um
16:00 Uhr
im
Raum 1008 (L1)
über das Thema:
Abstract: 
It is well known that when the geometry and/or coefficients allow stable trapped rays, the solution operator of the Helmholtz equation grows exponentially through a sequence of real frequencies tending to infinity. In this talk (based on the paper https://arxiv.org/abs/1903.12172 ) we show that, even in the presence of the strongest possible trapping, if a set of frequencies of arbitrarily small measure is excluded, the Helmholtz solution operator grows at most polynomially as the frequency tends to infinity. One significance application of this result is in the convergence analysis of several numerical methods for solving the Helmholtz equation at high frequency that are based on a polynomial growth assumption on the solution operator (e.g. hpfinite elements, hpboundary elements, certain multiscale methods). The result of this talk shows that this assumption holds, even in the presence of the strongestpossible trapping, for most frequencies. 
Hierzu ergeht herzliche Einladung. 
Prof. Dr. Daniel Peterseim 