A Stable Meshless Method for Electromagnetic Analysis

The major problem in applying a meshless (RPIM) method is that when a large number of sampling nodes is used, the condition number of the moment matrix increases, and numerical solution becomes unstable due to the required inversion of the matrix. To address the problem, in this paper, with the radial point interpolation meshless (RPIM) method as an example, the moment matrix is first diagonalized and then the associated singular eigenvalues that cause the instability are truncated. As a result, the dependence of the stability on the number of the sampling nodes is removed. Numerical experiments are conducted, and the results have shown that the proposed algorithm are stable irrespective of number of sampling nodes; they pay the way forward for the meshless method to be applied to practical structures.