The RBF partition of unity method for solving the Klein-Gordon equation

In this paper, a localized radial basis function (RBF) method is applied to obtain a global approximation of the solution of two dimensional Klein-Gordon equation on a given bounded domain. We use the RBF partition of unity (RBF-PU) method which is based on partitioning the original domain to several patches and using the RBF approximation on each local domain. Low computational cost and well conditioned final linear system are the main advantages of this method comparing with the original (global) RBF techniques. Numerical experiments show that the given problem could be solved successfully with a reasonable accuracy.

Automated summary

This paper applies a localized radial basis function (RBF) method to obtain a global approximation of the solution of the two dimensional Klein-Gordon equation on a given bounded domain. The RBF partition of unity (RBF-PU) method is used, which partitions the original domain into several patches and uses RBF approximation on each local domain. Numerical experiments demonstrate that the problem can be successfully solved with reasonable accuracy using this method, with advantages of low computational cost and well conditioned final linear system compared to global RBF techniques.