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arXiv · 2503.09580

A fast Fourier spectral method for the linearized Boltzmann collision operator

Tianai Yin·Zhenning Cai·Yanli Wang
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Abstract

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.

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Tianai Yin, Zhenning Cai, Yanli Wang. 2025-09-14. A fast Fourier spectral method for the linearized Boltzmann collision operator. https://arxiv.org/abs/2503.09580

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