Graduate Seminar "Aktuelle Themen der Numerik"

Thursday, Jun 05, 2014, 02:00 pm

Convolution Quadrature Methods for Time-Domain Wave Problems in BEM++

Dr. Timo Betcke (University College London)

Abstract:
A well-known approach to solving time-domain wave problems is to Laplace transform the wave equation, and then solve for a range of frequencies in the Laplace domain to synthesize the time-domain solution. Convolution Quadrature methods are a variant of this approach. Here, instead of Laplace transforming the wave equation we first apply a time-stepping method, and then perform a Z-Transform of the discrete time-steps to obtain a range of modified Helmholtz problems in the Laplace domain. We are in particular interested in solving wave problems in unbounded domains with this approach and present novel analytical results that highlight the convergence of the method with respect to the location of scattering poles of related Helmholtz problems. To implement Convolution Quadrature methods for wave problems in unbounded domains we use the boundary integral equation package BEM++, a novel open source library for a range of boundary integral equation problems, developed at UCL in collaboration with Reading and Warwick. We briefly introduce BEM++ and describe steps towards the development of a full time-domain toolbox for BEM++.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen