TY - JOUR
T1 - Comparison of Solvers for 2D Schrödinger Problems
AU - Gaspar , F. J.
AU - Rodrigo , C.
AU - Ciegis , R.
AU - Mirinavicius , A.
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 131
EP - 147
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/518.html
KW - finite difference method, Schrödinger problem, multigrid method, Alternating Direction Implicit method, Fast Fourier Transform method.
AB - <p style="text-align: justify;">This paper deals with the numerical solution of both linear and non-linear Schrödinger problems, which mathematically model many physical processes in a wide range of applications
of interest. In particular, a comparison of different solvers and different approaches for these
problems is developed throughout this work. Two finite difference schemes are analyzed: the
classical Crank-Nicolson approach, and a high-order compact scheme. Solvers based on geometric
multigrid, Fast Fourier Transform and Alternating Direction Implicit methods are compared.
Finally, the efficiency of the considered solvers is tested for a linear Schrödinger problem, proving
that the computational experiments are in good agreement with the theoretical predictions. In
order to test the robustness of the MG solver two additional Schrödinger problems with a nonconstant
potential and nonlinear right-hand side are solved by the MG solver, since the efficiency
of this solver depends on such data.</p>