SIMD-vectorized implicit symplectic integrators can outperform explicit ones
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908919869210624 |
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| author | Antoñana, Mikel Makazaga, Joseba Murua, Ander |
| author_facet | Antoñana, Mikel Makazaga, Joseba Murua, Ander |
| contents | The main purpose of this work is to present a SIMD-vectorized implementation of the symplectic 16th-order 8-stage implicit Runge-Kutta integrator based on collocation with Gauss-Legendre nodes (IRKGL16-SIMD), and to show that it can outperform state-of-the-art symplectic explicit integrators for high-precision numerical integrations (in double-precision floating-point arithmetic) of non-stiff Hamiltonian ODE systems. Our IRKGL16-SIMD integrator leverages Single Instruction Multiple Data (SIMD) based parallelism (in a way that is transparent to the user) to significantly enhance the performance of the sequential IRKGL16 implementation. We present numerical experiments comparing IRKGL16-SIMD with state-of-the-art high-order explicit symplectic methods for the numerical integration of several Hamiltonian systems in double-precision floating-point arithmetic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SIMD-vectorized implicit symplectic integrators can outperform explicit ones Antoñana, Mikel Makazaga, Joseba Murua, Ander Numerical Analysis The main purpose of this work is to present a SIMD-vectorized implementation of the symplectic 16th-order 8-stage implicit Runge-Kutta integrator based on collocation with Gauss-Legendre nodes (IRKGL16-SIMD), and to show that it can outperform state-of-the-art symplectic explicit integrators for high-precision numerical integrations (in double-precision floating-point arithmetic) of non-stiff Hamiltonian ODE systems. Our IRKGL16-SIMD integrator leverages Single Instruction Multiple Data (SIMD) based parallelism (in a way that is transparent to the user) to significantly enhance the performance of the sequential IRKGL16 implementation. We present numerical experiments comparing IRKGL16-SIMD with state-of-the-art high-order explicit symplectic methods for the numerical integration of several Hamiltonian systems in double-precision floating-point arithmetic. |
| title | SIMD-vectorized implicit symplectic integrators can outperform explicit ones |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2511.03655 |