Moving mesh methods for singular problems on a sphere using perturbed harmonic mappings

Yana Di*, Ruo Li, Tao TANG, Pingwen Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)1490-1508
Number of pages19
JournalSIAM Journal of Scientific Computing
Issue number4
Publication statusPublished - 2006

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Harmonic mapping
  • Moving mesh methods
  • Perturbed harmonic mapping
  • Singularity
  • Spherical domain


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