Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866913888351551488 |
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| author | Bazavov, Alexei |
| author_facet | Bazavov, Alexei |
| contents | A new format for commutator-free Lie group methods is proposed based on explicit classical Runge-Kutta schemes. In this format exponentials are reused at every stage and the storage is required only for two quantities: the right hand side of the differential equation evaluated at a given Runge-Kutta stage and the function value updated at the same stage. The next stage of the scheme is able to overwrite these values. The result is proven for a 3-stage third order method and a conjecture for higher order methods is formulated. Five numerical examples are provided in support of the conjecture. This new class of structure-preserving integrators has a wide variety of applications for numerically solving differential equations on manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_04225 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials Bazavov, Alexei Numerical Analysis High Energy Physics - Lattice Computational Physics A new format for commutator-free Lie group methods is proposed based on explicit classical Runge-Kutta schemes. In this format exponentials are reused at every stage and the storage is required only for two quantities: the right hand side of the differential equation evaluated at a given Runge-Kutta stage and the function value updated at the same stage. The next stage of the scheme is able to overwrite these values. The result is proven for a 3-stage third order method and a conjecture for higher order methods is formulated. Five numerical examples are provided in support of the conjecture. This new class of structure-preserving integrators has a wide variety of applications for numerically solving differential equations on manifolds. |
| title | Commutator-free Lie group methods with minimum storage requirements and reuse of exponentials |
| topic | Numerical Analysis High Energy Physics - Lattice Computational Physics |
| url | https://arxiv.org/abs/2007.04225 |