Using the RD rational Arnoldi method for exponential integrators
Paolo Novati
TL;DR
This paper explores the practical application of the RD rational Arnoldi method in exponential integrators for parabolic problems, providing bounds, implementation tips, and numerical experiments to improve computational efficiency.
Contribution
It introduces practical bounds and implementation strategies for the RD rational Arnoldi method within exponential integrators, supported by numerical experiments.
Findings
Derived useful a-posteriori bounds for the method
Provided implementation hints for integrators
Demonstrated effectiveness through numerical experiments
Abstract
In this paper we investigate some practical aspects concerning the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. We derive some useful a-posteriori bounds together with some hints for a suitable implementation inside the integrators. Numerical ex- periments arising from the discretization of sectorial operators are pre- sented.
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Taxonomy
TopicsNumerical methods for differential equations · Matrix Theory and Algorithms · Model Reduction and Neural Networks