Multiscale Methods and Stability in Some High-Frequency Helmholtz-Type Problems
Speaker: Donald Brown, School of Mathematical Sciences
Title: Multiscale Methods and Stability in Some High-Frequency Helmholtz-Type Problems
Abstract: In this talk, we will discuss issues in the computation of high-frequency Helmholtz-type problems. In particular, we discuss the issue of pollution effects and how certain multiscale sub-grid correction methods can eliminate the effect in certain resolution regimes. This will help to motivate the issue of frequency dependent stability in continuous problems. The frequency-dependent stability constants are critical to understanding the performance of the numerical algorithms, however, very few such explicit bounds exist in the literature. We will present a few of the current results on frequency explicit a-priori bounds for elastic media and heterogenous acoustic media. This work eliminates a critical assumption in previous attempts at bounds in elastodynamics problems, as well as established some initial bounds for the heterogenous Helmholtz case.