Accelerating Convolution Quadrature

Convolution quadtrature (CQ) is a method for discretizing continuous convolution integrals by substituting a discrete Z domain approximation for the Laplace domain frequency parameter s. The model CQ provides is inherently dispersive, and so gives rise to a discrete Green's function with expanding temporal support. This work investigates two approaches to alleviating this problem: dispersion halting and fast Fourier transform methods. Numerical results will be used to compare the methods with each other in both dispersive and nondispersive media.