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

Jens Markus Melenk, Alexander Rieder
2017 Journal of Integral Equations and Applications  
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 ^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
more » ... rate. Numerical experiments confirm the theoretical findings.
doi:10.1216/jie-2017-29-1-189 fatcat:xlrcwfugbjb3djvhv3ksjjxjee