Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
A modified Chebyshev pseudospectral method with an O(N–1) time step restriction
Journal of Computational Physics
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Terascale spectral element dynamical core for atmospheric general circulation models
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
A Schwarz Preconditioner for the Cubed-Sphere
SIAM Journal on Scientific Computing
Error Analysis for Mapped Legendre Spectral and Pseudospectral Methods
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs
SIAM Journal on Numerical Analysis
Fourth order partial differential equations on general geometries
Journal of Computational Physics
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Diffusion Equations over Arbitrary Triangulated Surfaces for Filtering and Texture Applications
IEEE Transactions on Visualization and Computer Graphics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
The Nonconvergence of $$h$$h-Refinement in Prolate Elements
Journal of Scientific Computing
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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.