Matrix equation techniques for certain evolutionary partial differential equations
Numerical Analysis
2020-03-18 v2 Numerical Analysis
Abstract
We show that the discrete operator stemming from the time and space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure of the involved coefficient matrices is proposed. The resulting scheme is able to efficiently solve problems with a tremendous number of degrees of freedom while maintaining a low storage demand as illustrated in several numerical examples.
Cite
@article{arxiv.1908.11851,
title = {Matrix equation techniques for certain evolutionary partial differential equations},
author = {Davide Palitta},
journal= {arXiv preprint arXiv:1908.11851},
year = {2020}
}