Paper Info
Title
Fourth-Order Time-Stepping For Stiff PDEs On The Sphere.
Abstract
We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with multiplication matrices that differ from the usual ones, and implicit-explicit time-stepping schemes. Operating in coefficient space with these new matrices allows one to use a sparse direct solver, avoids the coordinate singularity, and maintains smoothness at the poles, while implicit-explicit schemes circumvent severe restrictions on the time steps due to stiffness. A comparison is made against exponential integrators and it is found that implicit-explicit schemes perform best. Implementations in MATLAB and Chebfun make it possible to compute the solution of many PDEs to high accuracy in a very convenient fashion.
Year
DOI
Venue
2018
10.1137/17M1112728
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
stiff PDEs,exponential integrators,implicit-explicit,PDEs on the sphere,double Fourier sphere method,Chebfun
Mathematical optimization,Exponential integrator,Mathematical analysis,Matrix (mathematics),Fourier transform,Multiplication,Coordinate singularity,Solver,Smoothness,Mathematics,Unit sphere
Journal
Volume
Issue
ISSN
40
1
1064-8275
Citations 
PageRank 
References 
1
0.36
8
Authors
2
Name
Order
Citations
PageRank
Hadrien Montanelli1112.05
Yuji Nakatsukasa29717.74