A robust meshless method with QR-decomposed radial basis functions

Ill-condition of the interpolation matrix has presented a hurdle for applying a node-based meshless method to practical modeling and simulation of electromagnetic structures. In this paper, a robust meshless method is proposed that does not have the problem. It employs the QR method to decompose the Gaussian radial basis function; as a result, the matrix ill-condition that persists with a mesheless method with a small shape parameter is theoretically removed. In other words, unlike the conventional meshless method, the proposed method is insensitive to the shape parameters and can work well even when the radial basis functions becomes extremely flat.