A domain decomposition method for solving the hypersingular integral equation on the sphere with spherical splines

We present an overlapping domain decomposition technique for solving the hypersingular integral equation on the sphere with spherical splines. We prove that the condition number of the additive Schwarz operator is bounded by O(H/delta), where H is the size of the coarse mesh and delta is the overlap size, which is chosen to be proportional to the size of the fine mesh. In the case that the degree of the splines is even, a better bound O(1 + log(2)(H/delta)) is proved. The method is illustrated by numerical experiments on different point sets including those taken from magsat satellite data.