Journal of Integral Equations and Applications

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

Jens Markus Melenk and 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 $\mathbb{R}^d$, 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.

Article information

Source
J. Integral Equations Applications Volume 29, Number 1 (2017), 189-250.

Dates
First available in Project Euclid: 27 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1490583475

Digital Object Identifier
doi:10.1216/JIE-2017-29-1-189

Subjects
Primary: 65M38: Boundary element methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65R10: Integral transforms

Keywords
Convolution quadrature FEM-BEM coupling

Citation

Melenk, Jens Markus; Rieder, Alexander. Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation. J. Integral Equations Applications 29 (2017), no. 1, 189--250. doi:10.1216/JIE-2017-29-1-189. https://projecteuclid.org/euclid.jiea/1490583475.


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