Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917497875202048 |
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| author | Durastante, Fabio Mazza, Mariarosa |
| author_facet | Durastante, Fabio Mazza, Mariarosa |
| contents | We study energy-conserving Hamiltonian Boundary Value Methods (HBVMs) for Hamiltonian systems, which arise in applications where long-term preservation of energy and symplecticity is essential. HBVMs are multi-stage schemes whose stage equations reformulate as matrix equations with a low-rank right-hand side. For linear systems, we exploit this structure directly via Krylov projection solvers. For nonlinear systems, we leverage it within simplified Newton iterations and as a preconditioner in a Newton--Krylov framework, combined with adaptive time-stepping for robust convergence. Numerical experiments on semi-discretized wave equations demonstrate the efficiency and robustness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods Durastante, Fabio Mazza, Mariarosa Numerical Analysis 65F08, 65L06, 65F45 We study energy-conserving Hamiltonian Boundary Value Methods (HBVMs) for Hamiltonian systems, which arise in applications where long-term preservation of energy and symplecticity is essential. HBVMs are multi-stage schemes whose stage equations reformulate as matrix equations with a low-rank right-hand side. For linear systems, we exploit this structure directly via Krylov projection solvers. For nonlinear systems, we leverage it within simplified Newton iterations and as a preconditioner in a Newton--Krylov framework, combined with adaptive time-stepping for robust convergence. Numerical experiments on semi-discretized wave equations demonstrate the efficiency and robustness of the proposed approach. |
| title | Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods |
| topic | Numerical Analysis 65F08, 65L06, 65F45 |
| url | https://arxiv.org/abs/2511.21597 |