Solving large generalized interpolation problems efficiently
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posted on 2023-06-08, 08:20authored byHolger Wendland
In this paper we study generalized interpolation problems as they typically arise in the context of collocation methods for numerically solving partial differential equations, as well as in the theory of fluid-structure interaction. We concentrate on fast evaluation methods based upon a far field expansion of the underlying kernel, which will be a Gaussian. Finally, we show how the fast evaluation method can ultimately be combined with a domain decomposition method. Interpolation by radial basis functions (RBFs) or, more generally, (conditionally) positive definite kernels has proven to be an efficient tool in the context of function and surface reconstruction. But the flexibility of the approach allows to extend applications of RBFs to much more general.