Sparsity of Runge–Kutta convolution weights for the three-dimensional wave equation

Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge–Kutta based convolution quadratures. In this paper the behaviour of the weights of such quadratures is investigated. In particular approximate sparseness of their Galerkin discretization is analyzed. Further, it is demonstrated how these results can be used to construct and analyze the complexity of fast algorithms for the assembly of the fully discrete systems.