Convergence Studies for an Adaptive Meshless Least-Squares Collocation Method

Page:

377-386

DOI:

https://doi.org/10.2495/CMEM-V5-N3-377-386

OPEN ACCESS

Abstract:

In this paper, we apply the recently proposed fast block-greedy algorithm to a convergent kernel-based collocation method. In particular, we discretize three-dimensional second-order elliptic differential equations by the meshless asymmetric collocation method with over-sampling. Approximated solutions are obtained by solving the resulting weighted least squares problem. Such formulation has been proven to have optimal convergence in *H*2. Our aim is to investigate the convergence behaviour of some three dimensional test problems. We also study the low-rank solution by restricting the approximation in some smaller trial subspaces. A block-greedy algorithm, which costs at most *O(NK*2) to select *K *columns (or trial centers) out of an *M *× *N *overdetermined matrix, is employed for such an adaptivity. Numerical simulations are provided to justify these reductions.

Keywords:

*ansa method, kernel-based collocation, adaptive greedy algorithm, elliptic equation*

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