Rapid calculation of eddy current field Green's function using the matrix pencil method

The paper presents an efficient method to calculate dyadic Green's function of eddy current field in a conducting plate. The spectral domain integrands in vector potential are approximated by a short series of complex exponential functions, and the generalized Sommerfeld integrals (GSI) in vector potential can be evaluated as a closed-form expression. The poles and residues of integrands are obtained by using the matrix pencil method (MPM). The singular-value decomposition and total least-squares method are used to find the poles and residues accurately. An efficient technique of determining the sampling interval is presented. A closed-form expression of the spatial Green's function is obtained straightforward. The variations of different Green's function components with spatial coordinates are studied. The accuracy and calculation speed of the present method are compared with those of numerical integration. It is shown that this method can give an error of <1% at the distance between field-to-source point less than 5 skin depths, and achieve a computation speed of over 100 times faster than numerical integration.