An Analysis on Some Algorithms of Fast Runge-Kutta Convolution Quadrature: Efficient Numerical Solution for Time-Domain Boundary Integral Equations with Retarded Potentials using Fast Runge-Kutta Convolution Quadrature (Journal of Advances and Scholarly Researches in Allied Education, 2017)
This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.