3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach

We present a finite-element time-domain FETD approach for the simulation of 3D electromagnetic EM diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magneticfields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields,theelectricfielddiffusionequationistransformedinto asystemofdifferentialequationsviaGalerkin’smethodwith homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-inreducedorderingtechnique.Whenadvancingthesolution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current FEDCalgorithmthatsolvesPoisson’sequationusingasecondarypotentialmethodforageneralanisotropicearthmodel. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiencyofthe3DFETDalgorithm.

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