球谐熵用于最优3D建模

球面拓扑曲面平均曲率流的球谐伪谱方法

A spherical harmonic pseudo-spectral approach to mean curvature flow of surfaces with spherical topology

提出一种球谐伪谱方法求解球面拓扑闭曲面的平均曲率流，通过球谐函数离散化Dziuk方法的弱形式，证明位置误差的指数收敛性，数值实验验证理论结果。

球谐展开的快速算法，III

Fast algorithms for spherical harmonic expansions, III

利用蝴蝶方案加速球谐变换计算，通过深度优先遍历控制流图组织预计算，为多级过程提供高效替代方法。

关于球谐函数离散化中的最大值原理

On a maximum principle in discretization with spherical harmonics

本文针对球谐函数离散化中拉普拉斯方程的离散解不满足最大值原理的问题，推导了使离散解满足最大值原理的r_N^max的精确估计，并分析了估计的尖锐性。

FaVeST: Fast Vector Spherical Harmonic Transforms

Vector spherical harmonics on the unit sphere of $\mathbb{R}^3$ have broad applications in geophysics, quantum mechanics and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier coefficients of vector spherical harmonics. In this paper, we develop fast algorithms (FaVeST) for vector spherical harmonic transforms on these evaluations. The forward FaVeST evaluates the Fourier coefficients and has a computational cost proportional to $N\log \sqrt{N}$ for $N$ number of evaluation points. The adjoint FaVeST which evaluates a linear combi…

Vlasov-Poisson初边值问题的球谐展开

Spherical Harmonics Expansion of the Vlasov-Poisson initial bounary value problem

本文推导并分析了耦合能量的球谐展开（SHE）型方程组，证明了在长时间和大距离尺度上的扩散行为，并确定了扩散张量。

基于快速球谐变换的体积散射高效求解器

An efficient solver for volumetric scattering based on fast spherical harmonics transforms

提出一种基于快速球谐变换的O(N log N)高效求解器，用于求解Helmholtz方程的体积散射问题，通过Lippmann-Schwinger积分方程避免边界近似，收敛阶与解的正则性相关。