Space-time least squares approximation for Schr\"odinger equation and efficient solver
Numerical Analysis
2023-12-01 v1 Numerical Analysis
Abstract
In this work we present a space-time least squares isogeometric discretization of the Schr\"odinger equation and propose a preconditioner for the arising linear system in the parametric domain. Exploiting the tensor product structure of the basis functions, the preconditioner is written as the sum of Kronecker products of matrices. Thanks to an extension to the classical Fast Diagonalization method, the application of the preconditioner is efficient and robust w.r.t. the polynomial degree of the spline space. The time required for the application is almost proportional to the number of degrees-of-freedom, for a serial execution.
Cite
@article{arxiv.2311.18461,
title = {Space-time least squares approximation for Schr\"odinger equation and efficient solver},
author = {Andrea Bressan and Alen Kushova and Giancarlo Sangalli and Mattia Tani},
journal= {arXiv preprint arXiv:2311.18461},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1909.07309