A novel Galerkin method for solving PDES on the sphere using highly localized kernel bases Academic Article uri icon

abstract

  • © 2016 American Mathematical Society. The main goal of this paper is to introduce a novel rncshless kernel Galerkin method for numerically solving partial differential equations on the sphere. Specifically, we will use this method to treat the partial differential equation for stationary heat conduction on S2, in an inhomogeneous, anisotropic medium. The Galerkin method used to do this employs spatially well-localized, "small footprint", robust bases for the associated kernel space. The stiffness matrices arising in the problem have entries decaying exponentially fast away from the diagonal. Discretization is achieved by first zeroing out small entries, resulting in a sparse matrix, and then replacing the remaining entries by ones computed via a very efficient kernel quadrature formula for the sphere. Error estimates for the approximate Galerkin solution are also obtained.

author list (cited authors)

  • Narcowich, F. J., Rowe, S. T., & Ward, J. D.

citation count

  • 10

publication date

  • March 2016