Stability of Discretized Partial Element Equivalent EFIE Circuit Models

The instabilities associated with integral equation techniques for the solution of electromagnetic problems in the time domain are well known. Instabilities may be due to either the numerical technique used for the time integration, or problems created by the discrete representation for the numerical solution of the problem. In this paper, we concentrate on the discretization issue. The stability problem occurs for various discretizations and formulations. Here, we use the partial element equivalent circuit (PEEC) formulation of the electric field integral equation (EFIE) in the circuit domain. This leads to a better understanding of the issues at hand. We show why the discretized model can be unstable and we suggest a circuit motivated technique to stabilize the solution. © 1995 IEEE