Runge-Kutta convolution quadrature and FEM-BEM coupling for the time dependent linear Schrödinger equation
Provides a stable and convergent numerical method for solving the Schrödinger equation on unbounded domains, benefiting computational scientists in quantum mechanics.
The paper proposes a numerical scheme for the time-dependent linear Schrödinger equation using Runge-Kutta time-stepping and FEM-BEM coupling, proving stability and convergence rates, with numerical experiments confirming theory.
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 $\R^d$ 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.