From Memory Model to CPU Time: Exponential Integrators for Advection-Dominated Problems
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908690916835328 |
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| author | Dang, Thi Tam Hoang, Trung Hau |
| author_facet | Dang, Thi Tam Hoang, Trung Hau |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_03679 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Memory Model to CPU Time: Exponential Integrators for Advection-Dominated Problems Dang, Thi Tam Hoang, Trung Hau Numerical Analysis 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. |
| title | From Memory Model to CPU Time: Exponential Integrators for Advection-Dominated Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.03679 |