Wavelets and convolution quadrature for the efficient solution of a 2D space-time BIE for the wave equation

摘要

We consider a wave propagation problem in 2D, reformulated in terms of a Boundary Integral Equation (BIE) in the space-time domain. For its solution, we propose a numerical scheme based on a convolution quadrature formula by Lubich for the discretization in time, and on a Galerkin method in space. It is known that the main advantage of Lubich's formulas is the use of the FFT algorithm to retrieve discrete time integral operators with a computational complexity of order R log R, R being twice the total number of time steps performed. Since the discretization in space leads in general to a quadratic complexity, the global computational complexity is of order (MR)-R-2 log R and the working storage required is (MR)-R-2/2, where M is the number of grid points on the domain boundary.