Abstract
This work is concerned with developing moving mesh strategies for solving problems defined on a sphere. To construct mappings between the physical domain and the logical domain, it has been demonstrated that harmonic mapping approaches are useful for a general class of solution domains. However, it is known that the curvature of the sphere is positive, which makes the harmonic mapping on a sphere not unique. To fix the uniqueness issue, we follow Sacks and Uhlenbeck [Ann. of Math. (2), 113 (1981), pp. 1-24] to use a perturbed harmonic mapping in mesh generation. A detailed moving mesh strategy including mesh redistribution and solution updating on a sphere will be presented. The moving mesh scheme based on the perturbed harmonic mapping is then applied to the moving steep front problem and the Fokker-Planck equations with high potential intensities on a sphere. The numerical experiments show that with a moderate number of grid points our proposed moving mesh algorithm can accurately resolve detailed features of singular problems on a sphere.
Original language | English |
---|---|
Pages (from-to) | 1490-1508 |
Number of pages | 19 |
Journal | SIAM Journal of Scientific Computing |
Volume | 28 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2006 |
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics
User-Defined Keywords
- Harmonic mapping
- Moving mesh methods
- Perturbed harmonic mapping
- Singularity
- Spherical domain