Radial basis function methods: living in a meshfree world

Alfa Heryudono

UMass Dartmouth

Since their first applications in scattered data interpolation on irregular surfaces in the 70's, RBF methods have become increasingly popular for the numerical solution of PDEs. The methods are relatively simple to implement without mesh or special grids, independent of dimensions, and extensible to be hybridized with other methods. This talk will cover practical implementation of RBF methods related to interpolation, nodes adaptivity, and PDE collocation in finite difference and partition of unity modes. We present numerical experiments showing spectral convergence with respect to the local problem resolution and algebraic convergence with respect to the partition size. Several simulations in MATLAB will be shown. (joint work with Elisabeth Larsson (Uppsala) and Toby Driscoll (Delaware) )

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