“Effect of background fields on three-dimensioanal finite element analysis of induction logging,” Radio Science, Vol. 36, No. 4, pp. 721-729, 2001.
Three‐dimensional controlled‐source electromagnetic induction algorithms are generally formulated in terms of secondary fields or potentials. The selection of the primary solution is somewhat arbitrary but can greatly influence the efficiency of finite element codes. A simple induction logging problem demonstrates this statement. Responses are computed using a three‐dimensional finite element method for two different selections of the primary potential, one that includes the borehole effect and one that does not. The accuracy of the numerical solution, for a given mesh size, increases dramatically when the borehole effect is included in the primary solution. This is because the sharp gradients in the electromagnetic field near the transmitter due to the presence of the borehole are coded as an analytic source term and do not have to be captured by the numerical approximation. Whenever possible, finite element analysts should select a convenient primary solution that closely matches the anticipated total solution in the immediate vicinity of the transmitter.