High-Order nyström/Convolution-Quadrature solution of time-Domain scattering from closed and open lipschitz boundaries with dirichlet and neumann boundary conditions

Abstract

We investigate high-order Convolution Quadratures methods for the solution of the wave equation in the exterior of two dimensional and axi-symmetric three dimensional scatterers that rely on Nyström discretizations for the Boundary Integral Equation formulations of the ensemble of associated Laplace domain modified Helmholtz problems. Both Dirichlet and Neumann boundary conditions, imposed on open-arc/open surfaces as well as Lipschitz closed scatterers, are considered. Two classes of CQ discretizations are employed, one based on linear multistep methods and the other based on Runge-Kutta methods, in conjunction with Nyström discretizations based on Alpert and QBX quadratures of Boundary Integral Equation (BIE) formulations of the Laplace domain Helmholtz problems with complex wavenumbers. A variety of accuracy tests are presented that showcase the high-order in time convergence (up to and including fifth order) that the Nyström CQ discretizations are capable of delivering and we compare to numerical results in the literature pertaining to time-domain multiple scattering problems solved with other methods.