学术报告报告主题: A fast Fourier spectral method for wave kinetic equation
报 告 人: 綦昆仑 博士
报告时间：2025年6月6日（星期五）上午11:05-11:50
报告地点：37号楼3A01
邀 请 人: 温焕尧教授
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数学学院
2025年6月3日
报告摘要：
The central object in wave turbulence theory is the wave kinetic equation (WKE), which is an evolution equation for wave action density and acts as the wave analog of the Boltzmann kinetic equations for particle interactions. Despite recent exciting progress in the theoretical aspects of the WKE, numerical developments have lagged behind. In this talk, I will introduce a fast Fourier spectral method for solving the WKE. The key idea lies in reformulating the high-dimensional nonlinear wave kinetic operator as a spherical integral, analogous to the classical Boltzmann collision operator. The conservation of mass and momentum leads to a double convolution structure in Fourier space, which can be efficiently handled by the fast Fourier transform (FFT). The accuracy and efficiency of the proposed method can be demonstrated through several numerical tests in both 2D and 3D, revealing and conjecturing some interesting and unique features of this equation.
报告人介绍：
綦昆仑2017年本科毕业于华南理工大学数学学院，2021年7月博士毕业于香港城市大学，师从杨彤教授。2021年7月-2022年7月于香港中文大学进行博士后研究工作，并于2022年8月至今加入明尼苏达大学数学学院担任Dunham-Jackson助理教授(non-tenure track)。其研究方向集中于动理学理论(Kinetic Theory)，尤其是玻尔兹曼方程及其相关流体、材料模型的多尺度建模，数值模拟和误差分析，相关成果发表在SIAM J. Numer. Anal., SIAM J. Appl. Math., SIAM Multiscale Model. Simul., M3AS, JCP等期刊。