A fast Fourier spectral method for the linearized Boltzmann collision operator
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908536293818368 |
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| author | Yin, Tianai Cai, Zhenning Wang, Yanli |
| author_facet | Yin, Tianai Cai, Zhenning Wang, Yanli |
| contents | We introduce a fast Fourier spectral method to compute linearized collision operators of the Boltzmann equation for variable hard-sphere gases. While the state-of-the-art method provides a computational cost O(MN^4 log N), with N being the number of modes in each direction and M being the number of quadrature points on a hemisphere, our method reduces the cost to O(N^4 log N), removing the factor M, which could be large in our numerical tests. The method is applied in a numerical solver for the steady-state Boltzmann equation with quadratic collision operators. Numerical experiments for both spatially homogeneous and inhomogeneous Boltzmann equations have been carried out to test the accuracy and efficiency of our method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09580 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A fast Fourier spectral method for the linearized Boltzmann collision operator Yin, Tianai Cai, Zhenning Wang, Yanli Numerical Analysis Analysis of PDEs 65M70, 76P05, 35Q20 We introduce a fast Fourier spectral method to compute linearized collision operators of the Boltzmann equation for variable hard-sphere gases. While the state-of-the-art method provides a computational cost O(MN^4 log N), with N being the number of modes in each direction and M being the number of quadrature points on a hemisphere, our method reduces the cost to O(N^4 log N), removing the factor M, which could be large in our numerical tests. The method is applied in a numerical solver for the steady-state Boltzmann equation with quadratic collision operators. Numerical experiments for both spatially homogeneous and inhomogeneous Boltzmann equations have been carried out to test the accuracy and efficiency of our method. |
| title | A fast Fourier spectral method for the linearized Boltzmann collision operator |
| topic | Numerical Analysis Analysis of PDEs 65M70, 76P05, 35Q20 |
| url | https://arxiv.org/abs/2503.09580 |