A Prolate-Element Method for Nonlinear PDEs on the Sphere

作者：Zhang Jing; Wang Li Lian^*; Rong Zhijian

来源：Journal of Scientific Computing, 2011, 47(1): 73-92.

DOI：10.1007/s10915-010-9421-y

• Bandlimited basis
• Prolate-Gauss-Lobatto points
• Cube-sphere transform
• Spectral-element method
• Quasi-uniform grids

A p-type spectral-element method using prolate spheroidal wave functions (PSWFs) as basis functions, termed as the prolate-element method, is developed for solving partial differential equations (PDEs) on the sphere. The gridding on the sphere is based on a projection of the prolate-Gauss-Lobatto points by using the cube-sphere transform, which is free of singularity and leads to quasi-uniform grids. Various numerical results demonstrate that the proposed prolate-element method enjoys some remarkable advantages over the polynomial-based element method: (i) it can significantly relax the time step size constraint of an explicit time-marching scheme, and (ii) it can increase the accuracy and enhance the resolution.

• 出版日期2011-4
• 单位厦门大学; 南阳理工学院