Multiscale RBF collocation for solving PDEs on spheres |
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Authors: | Email author" target="_blank">Q?T?Le GiaEmail author I?H?Sloan H?Wendland |
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Institution: | 1.School of Mathematics and Statistics,University of New South Wales,Sydney,Australia;2.Mathematical Institute,University of Oxford,Oxford,UK |
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Abstract: | In this paper, we discuss multiscale radial basis function collocation methods for solving certain elliptic partial differential
equations on the unit sphere. The approximate solution is constructed in a multi-level fashion, each level using compactly
supported radial basis functions of smaller scale on an increasingly fine mesh. Two variants of the collocation method are
considered (sometimes called symmetric and unsymmetric, although here both are symmetric). A convergence theory is given,
which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. |
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Keywords: | |
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