Translator Disclaimer
2017 Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation
Jens Markus Melenk, Alexander Rieder
J. Integral Equations Applications 29(1): 189-250 (2017). DOI: 10.1216/JIE-2017-29-1-189

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.

Citation

Download Citation

Jens Markus Melenk. Alexander Rieder. "Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation." J. Integral Equations Applications 29 (1) 189 - 250, 2017. https://doi.org/10.1216/JIE-2017-29-1-189

Information

Published: 2017
First available in Project Euclid: 27 March 2017

zbMATH: 1361.65076
MathSciNet: MR3628111
Digital Object Identifier: 10.1216/JIE-2017-29-1-189

Subjects:
Primary: 65M38, 65N30, 65R10

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
62 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.29 • No. 1 • 2017
Back to Top