MLegS：一个用于无界域并行的现代映射勒让德谱方法求解器
MLegS: A modern mapped Legendre spectral method solver for unbounded domains with parallelization
- Nanyang Technological University（南洋理工大学）
- University of California, Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
MLegS是一个开源现代Fortran谱方法求解器，通过映射连带勒让德基和MPI并行处理径向无界域上的PDE，在扩散、反应扩散和涡旋动力学中验证了谱收敛、前沿速度和Crow增长率。
AI中文摘要：
MLegS是一个开源的现代Fortran代码包，用于在径向无界域上求解线性和非线性含时偏微分方程。它基于早期的内部原型构建，将其重构为一个模块化求解器，为场、变换和谱算子提供统一接口。在该框架内，数值公式将$0\leq r<\infty$映射到有限区间，其中连带勒让德函数提供径向基，而傅里叶级数表示周期性的方位角和轴向方向。映射的径向基表示径向无穷远，而无需在有限半径处施加人工边界条件，同时根据方位角阶数纳入$r=0$处所需的正则性。该实现使用消息传递接口（MPI）分布相应的场布局，强扩展和弱扩展测量扩展到四个计算节点上的512个核心。除并行性能外，三个示例评估了求解器在扩散、反应-扩散和涡旋动力学方面的表现：闭式扩散解确立了谱空间收敛性以及两种半隐式积分器的设计阶数；Fisher-Kolmogorov-Petrovsky-Piskunov前沿与线性化解匹配，并在其对数修正内以经典速度传播；基于环向-极向分解的涡旋对模拟测得的Crow增长率比理论预测高$2.7\\%$，并展示了涡旋对的重新连接。
英文摘要：
MLegS is an open-source Modern Fortran code package for solving linear and nonlinear time-dependent partial differential equations on radially unbounded domains. It builds on an earlier in-house prototype, recasting it as a modular solver with a unified interface for fields, transforms, and spectral operators. Within this framework, the numerical formulation maps $0\leq r<\infty$ onto a finite interval, where associated Legendre functions provide the radial basis, while Fourier series represent the periodic azimuthal and axial directions. The mapped radial basis represents radial infinity without imposing an artificial boundary condition at finite radius while incorporating the regularity required at $r=0$ according to azimuthal order. The implementation distributes the corresponding field layouts using the Message-Passing Interface (MPI), with strong- and weak-scaling measurements extending to 512 cores across four compute nodes. Beyond parallel performance, three examples assess the solver across diffusion, reaction-diffusion, and vortex dynamics: closed-form diffusion solutions establish spectral spatial convergence and the design orders of both semi-implicit integrators; a Fisher-Kolmogorov-Petrovsky-Piskunov front matches the linearized solution and propagates at the classical speed within its logarithmic correction; and vortex-pair simulations based on toroidal-poloidal decomposition yield a measured Crow growth rate $2.7\%$ above the theoretical prediction and demonstrate the reconnection of the vortex pair.
