Numerical solutions to a boundary-integral equation with spherical radial basis functions

Abstract

The Laplace equation in the exterior of the unit sphere with a Dirichlet boundary condition arises from geodesy, oceanography and meteorology. This problem is reformulated into a weakly singular integral equation on the sphere. We study the use of spherical radial basis functions to find approximate solutions to this integral equation using collocation methods. Experiments with data collected by a NASA satellite are performed to clarify the method. Our results illustrate how scattered data can be handled when solving boundary value problems in the exterior of the sphere. References

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