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 - <p style="text-align: justify;">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.</p>