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arXiv · 1605.07340

Runge-Kutta convolution quadrature and FEM-BEM coupling for the time dependent linear Schr\"odinger equation

Jens Markus Melenk·Alexander Rieder
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Abstract

We propose a numerical scheme to solve the time dependent linear Schr\"odinger equation. The discretization is carried out by combining a Runge-Kutta time-stepping scheme with a finite element discretization in space. Since the Schr\"odinger 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.

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Jens Markus Melenk, Alexander Rieder. 2016-05-24. Runge-Kutta convolution quadrature and FEM-BEM coupling for the time dependent linear Schr\"odinger equation. https://doi.org/10.1216/jie-2017-29-1-189

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