Multiscale RBF collocation for solving PDEs on spheres (Q415517)

The authors develop a multiscale approximation for elliptic partial differential equations (PDEs) on the unit sphere. Two variants of the collocation methods are presented for solving elliptic PDEs on the unit sphere using the radial basis functions (RBFs) of a single scale. The corresponding multiscale methods are presented. A convergence theorem for the multiscale methods is proved. At the end some numerical examples are discussed.