Year: 2025
Type: preprint
Abstract: In this paper, we investigate the application of exponential integrators to advection-dominated problems. We focus on Krylov subspace and Leja interpolation methods to compute the action of exponential and related matrix functions. Complementing our earlier paper, arXiv:2410.12765 (to appear in Advances in Applied Mathematics and Mechanics, 2025) based on a performance model, we extend the numerical investigation to higher-order Krylov approximations and new numerical regime, and assess their CPU-time efficiency relative to explicit Runge--Kutta schemes. We show that, depending on the problem setting, exponential integrators can either outperform or match explicit Runge--Kutta schemes. We also observe that Leja-based methods outperform Krylov iterations for large time steps, whereas for small time steps, Krylov-based methods provide better results than Leja-based methods.
Source: arXiv (Cornell University)
Authors: Dang, Thi Tam, Hoang, Trung Hau
Institutions: University of Helsinki, Universität Innsbruck
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417030971
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