Adaptive meshless refinement schemes for RBF-PUM collocation

On Adaptive Unsymmetric Meshless Collocation

The set Λ consists of infinitely many linear real–valued functionals λ that usually take the form of point evaluations of functions or derivatives at points inside a domain or on some boundary or interface layer. If several differential or boundary operators are involved, we simply put everything into a single set Λ of functionals of various types. We call (1) a generalized interpolation proble...

Adaptive meshless centres and RBF stencils for Poisson equation

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the me...

H-Adaptive Local Radial Basis Function Collocation Meshless Method

This paper introduces an effective H-adaptive upgrade to solution of the transport phenomena by the novel Local Radial Basis Function Collocation Method (LRBFCM). The transport variable is represented on overlapping 5-noded influence-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the variable are calculated from the ...

OpenCL Based Parallel Algorithm for RBF-PUM Interpolation

We present a new parallel algorithm for multivariate RBF-PUM interpolation. • The nature of the PUM allows to deal with a large number of scattered data-points in high space dimensions. • Our algorithm makes use of shared-memory parallel processors through the OPENCL standard [3]. • This parallel strategy gives a linear computational time complexity with respect to the number of data-points. • ...

Adaptive Local Grid Refinement Algorithms for Finite-element Collocation