Abstract
We propose an adaptive meshless discretization method to solve the 2D elliptic equations using the radial basis function (RBF) interpolation. To enhance the efficiency of the method, we introduce the error indicator threshold for the meshless adaptive refinement, and a 2-phase center selection strategy with variable number of centers. The algorithm presented in this paper significantly improves our earlier algorithms in [6] and [21], in that the accuracy, stability, and efficiency of its approximation solutions are better for problems with rapid oscillation or with complex geometries. Moreover, our experiments show that the computational cost of the algorithm significantly decreases as the number of centers increases. In particular, the average stencil size is less than 6, which leads to a higher sparsity of the system matrix, and so the computational cost is reduced.
Published Version
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