Speaker
Heather Wilber, University of Washington
Abstract
This talk will discuss two applications where improved computational methods are developed via contour integration techniques. The first application tackles the the acoustic wave equation in an exterior domain. This problem is challenging to solve with traditional time-stepping methods, especially in cases where the domain includes corners and trapping regions. One way to avoid many of these problems is to express the solution as an inverse Fourier transform of the multifrequency Helmholtz equation. Employing an early observation of Rokhlin (1983), we perturb the frequency parameter into the complex plane and use contour integration to make this approach computationally tractable, even in the presence of strong trapping. For the second application, we consider the use of proxy point methods for a broad class of 2D kernel functions. How does one choose quasi-optimal proxy points, and can we meaningfully bound the minimal number of proxy points required to achieve a specified accuracy? Through the lens of contour integration and rational approximation, these questions can be answered.