A pseudospectral approach for polar and spherical geometries
SIAM Journal on Scientific Computing
Fast Shallow-Water equation solvers in latitude-longitude coordinates
Journal of Computational Physics
Double Fourier series on a sphere: applications to elliptic and vorticity equations
Journal of Computational Physics
Spectral methods in MatLab
Generalized discrete spherical harmonic transforms
Journal of Computational Physics
Computational harmonic analysis for tensor fields on the two-sphere
Journal of Computational Physics
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
A performance comparison of associated Legendre projections
Journal of Computational Physics
Fast spin ±2 spherical harmonics transforms and application in cosmology
Journal of Computational Physics
GNU Scientific Library Reference Manual - Third Edition
GNU Scientific Library Reference Manual - Third Edition
Journal of Computational Physics
An Improved Magma Gemm For Fermi Graphics Processing Units
International Journal of High Performance Computing Applications
Hi-index | 31.45 |
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation.