Runge-Kutta convolution quadrature and FEM-BEM coupling for the time dependent linear Schrödinger equation

Abstract

We propose a numerical scheme to solve the time dependent linear Schrödinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a finite element discretization in space. Since the Schrödinger equation is posed on the whole space ${\mathbb{R}}^d$ we combine the interior finite element discretization with a convolution quadrature based boundary element discretization. In this paper we analyze the resulting fully discrete scheme in terms of stability and convergence rate. Numerical experiments confirm the theoretical findings.

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