A time-domain collocation meshless method with local radial basis functions for electromagnetic transient analysis

A meshless method with local radial basis functions is proposed for solving the time-domain electromagnetic wave equations. In comparison with the conventional radial point interpolation meshless (RPIM) method that employs and positions dual sets of nodes of both electric and magnetic field nodes, the proposed method uses only one set of the nodes, electric field nodes where electric fields are also collocated in space. With this feature, implementation complexity of the RPIM method is significantly reduced, and conformal modeling and muti-scale capabilities of the RPIM method can now be further explored with higher efficiency. The time-marching formulations of the proposed method are derived and stability analysis of the method is presented. Comparisons of the proposed method with the conventional meshless method are also presented. The accuracy and efficiency of the proposed method are demonstrated through simulation of an H-shaped cavity and a quarter ring resonator.