A theoretical and numerical analysis of the measured equation of invariance

The measured equation of invariance (MEI) has been previously introduced to efficiently and accurately handle the boundary truncation for finite methods. The present authors give a theoretical analysis that provides several important insights into the capabilities of the MEI. From the numerical study, they can explain why the MEI works better than one would expect. Both the theoretical and the numerical analyses demonstrate that the accuracy of the solution is dependent on the electrical size of the geometry as well as the distance between the mesh boundary and the geometry. From the analysis, the authors propose a new set of metrons that is less sensitive to the excitation than the previously proposed sinusoidal metrons.