Fasshauer GE Meshfree Approximation Methods with Matlab. Chen W Fu Z-J Chen CS Recent Advances on Radial Basis Function Collocation Methods 2014 Berlin Springer Google Scholar Cavoretto R De Rossi A Adaptive meshless refinement schemes for RBF-PUM collocation Appl.

Holger Wendland: Scattered data approximation.

Fasshauer: Meshfree approximation methods with MATLAB. Hilfsmittel: ein doppelseitig beschriebenes DIN A4-Blatt.

change to the kdtree directory, compile by, e.g.

at the MATLAB prompt, type 'mex -setup' in order to set up the compiler ('doc mex' for options).

kdtree and sdist.m, MEX versions (faster).

Problem 6.1: 2D cardinal basis functions.

Chapter 6: Native space error estimates.

Problem 4.8: meshfree 2D interpolation with compactly supported RBFs.Problem 4.7: interpolation error in dependence of shape parameter.Problem 4.5: interpolation with compactly supported RBFs.Chapter 3: Completely monotone functions.Problem 2.11: interpolation with inverse multi quadrics RBFs.Problem 1.7: interpolation with Gaussian RBFs.Problem 1.5: 2D interpolation with euclidean distance basis functions.Problem 1.4: error in dependence of the number of knots.Problem 1.3: 1D interpolation with euclidean distance basis functions.Will be intertwined with programming exercises in MATLAB.

This lecture will cover the basics of meshfree methods with an emphasis on approximation by radial basis functions. These methods are very flexible with respect to the geometry of the domain, work in higher space dimensions and their basic implementation is strikingly simple. In contrast to more traditional techniques - like finite differences, finite elements, spectral methods or wavelets - they do not require a mesh of the underlying computational domain (where the unknown function lives) to be generated first. Meshfree methods are a comparatively new approach for the (numerical) interpolation or approximation of some unknown function.

Fasshauer meshfree methods chaper 14