A 3-D finite‐element solution has been used to solve controlled‐source electromagnetic (EM) induction problems in heterogeneous electrically conducting media. The solution is based on a weak formulation of the governing Maxwell equations using Coulomb‐gauged EM potentials. The resulting sparse system of linear algebraic equations is solved efficiently using the quasi‐minimal residual method with simple Jacobi scaling as a preconditioner. The main aspects of this work include the implementation of a 3-D cylindrical mesh generator with high‐quality local mesh refinement and a formulation in terms of secondary EM potentials that eliminates singularities introduced by the source. These new aspects provide quantitative induction‐log interpretation for petroleum exploration applications. Examples are given for 1-D, 2-D, and 3-D problems, and favorable comparisons are presented against other, previously published multidimensional EM induction codes. The method is general and can also be adapted for controlled‐source EM modeling in mining, groundwater, and environmental geophysics in addition to fundamental studies of EM induction in heterogeneous media.
Magnetic resonance imaging (MRI), as well as some volume selected spectroscopy methods, use pulsed magnetic field gradients which induce multi-exponentially decaying eddy currents in all nonlaminated conductive parts of the superconducting magnets. This paper presents the analysis of the z gradient field distorsion due to the induced eddy currents and the corresponding correction in a 4 T / 30 c m bore superferric self-shielded magnet.
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The paper presents a numerical procedure based on the finite element method to determine the performance of ferrite-type permanent magnet DC motors. Magnetic saturation, armature's displacement and temperature's effect were considered in the computation Qf the torque's variation with respect t o angular position. and coercivity [l]:The risk of demagnetization is bigger at low temperatures, where the remanent induction B,,, is high and the coercive force H,,,, is low. The B -H loop changes are reversible and linear over a limited range (0 -120)' C.Correspondingly, a linear approximation was used to determine the temperature coefficients for both remanence .
Abstract. 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 e•ciency 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.
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