Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces
For researchers in computational acoustics and electromagnetics, this provides a novel method to handle time-domain scattering from unbounded penetrable interfaces, a previously challenging problem.
This paper develops boundary integral equation methods for time-domain scattering from unbounded penetrable interfaces, combining Convolution Quadrature with the Windowed Green Function method to achieve super-algebraically fast convergence with window size. Numerical examples demonstrate the approach's effectiveness for wave propagation in open waveguides and multiply layered media.
This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two-spatial dimensions. The proposed methodology relies on Convolution Quadrature (CQ) methods in conjunction with the recently introduced Windowed Green Function (WGF) method. As in standard time-domain scattering from bounded obstacles, a CQ method of the user's choice is utilized to transform the problem into a finite number of (complex) frequency-domain problems posed on the domains involving penetrable unbounded interfaces. Each one of the frequency-domain transmission problems is then formulated as a second-kind integral equation that is effectively reduced to a bounded interface by means of the WGF method---which introduces errors that decrease super-algebraically fast as the window size increases. The resulting windowed integral equations can then be solved by means of any (accelerated or unaccelerated) off-the-shelf Helmholtz boundary integral equation solver capable of handling complex wavenumbers with a large imaginary part. A high-order Nyström method based on Alpert quadrature rules is utilized here. A variety of numerical examples including wave propagation in open waveguides as well as scattering from multiply layered media demonstrate the capabilities of the proposed approach.