A comparison of analytical and numerical results for a 2‐D control model in electromagnetic induction ‐ II. E‐polarization calculations

Abstract

The 2‐D model proposed in an earlier paper as a control on the accuracy of numerical modelling programs operating in the B‐polarization mode, is used here to test the corresponding E‐polarization calculations. The model comprises a conducting slab divided into three segments of different conductivities and overlying a perfect conductor. The control solution is obtained in the E‐polarization mode by a ‘quasi‐analytic’ method in which a 1‐D integral equation satisfied by the horizontal magnetic field on the surface of the conductor is solved by the method of successive approximations. Values of all the field components for a particular set of modei parameters are calculated by this method at selected points on the surface of the conductor and on a horizontal plane inside the conductor. As in the previous paper, these values are used to check the accuracy of results given by (i) the finite difference program of Brewitt‐Taylor & Weaver in which improved finite difference formulae for calculating the derived magnetic field components have been incorporated and (ii) the finite element program of Kisak & Silvester. The finite difference program gives results in remarkably close agreement with the analytic solution; relative errors in all the field components are generally less than 1 per cent. The finite element program does not perform as well. In particular it gives errors of around 10 per cent in the values of the vertical magnetic field near the segment boundaries. It appears that the finite element program is not suitable for models which have different 1‐D conductivity distributions at infinity on the lhs and rhs. Copyright © 1986, Wiley Blackwell. All rights reserved