Volume 20, Issue 1
A Time-Space Adaptive Method for the Schrödinger Equation

Katharina Kormann

Commun. Comput. Phys., 20 (2016), pp. 60-85.

Published online: 2018-04

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  • Abstract

In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.

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@Article{CiCP-20-60, author = {}, title = {A Time-Space Adaptive Method for the Schrödinger Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {1}, pages = {60--85}, abstract = {

In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.101214.021015a}, url = {http://global-sci.org/intro/article_detail/cicp/11145.html} }
TY - JOUR T1 - A Time-Space Adaptive Method for the Schrödinger Equation JO - Communications in Computational Physics VL - 1 SP - 60 EP - 85 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.101214.021015a UR - https://global-sci.org/intro/article_detail/cicp/11145.html KW - AB -

In this paper, we present a discretization of the time-dependent Schrödinger equation based on a Magnus-Lanczos time integrator and high-order Gauss-Lobatto finite elements in space. A truncated Galerkin orthogonality is used to obtain duality-based a posteriori error estimates that address the temporal and the spatial error separately. Based on this theory, a space-time adaptive solver for the Schrödinger equation is devised. An efficient matrix-free implementation of the differential operator, suited for spectral elements, is used to enable computations for realistic configurations. We demonstrate the performance of the algorithm for the example of matter-field interaction.

Katharina Kormann. (2020). A Time-Space Adaptive Method for the Schrödinger Equation. Communications in Computational Physics. 20 (1). 60-85. doi:10.4208/cicp.101214.021015a
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