SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 273-294, February 2024.
Abstract. This paper presents a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method and prove that it maintains spectral accuracy. To solve the optimization problem, we propose an efficient Newton solver that has a quadratic convergence rate. Numerical examples are provided to demonstrate the high accuracy of the proposed method. Our method is also integrated into the spectral solver of the Boltzmann equation, showing the benefit of our approach in applications.

中文翻译：

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一种正矩保持傅里叶谱方法

SIAM 数值分析杂志，第 62 卷，第 1 期，第 273-294 页，2024 年 2 月。
摘要。本文提出了一种新颖的傅里叶谱方法，该方法利用优化技术来确保三角多项式空间中矩的正性和守恒性。我们严格分析了新方法的准确性，并证明它保持了光谱精度。为了解决优化问题，我们提出了一种具有二次收敛速度的高效牛顿求解器。提供了数值例子来证明该方法的高精度。我们的方法还集成到玻尔兹曼方程的谱求解器中，显示了我们的方法在应用中的优势。