A finite-element time-domain (FETD) electromagnetic forward solver for a complex-shaped transmitting loop is presented. Any complex-shaped source can be viewed as a combination of electric dipoles (EDs), each of which can be further decomposed into two horizontal EDs along the x- and y-directions and one vertical ED along the z-direction. Using this method, a complex-shaped loop can be easily handled when implementing an FE method based on the total-field algorithm and an unstructured tetrahedral mesh. The FETD solver that we developed used a vector FE method and the first-order backward Euler method to discretize in space and time, respectively. Unstructured tetrahedral girds combined with a local refinement technique was used to exactly delineate topography and a deformed loop. This FETD solver was tested by the five following scenarios: a rectangular loop on a flat-surface half-space, a circular loop on a stratified medium, a rectangular loop laid on a slope-surface half-space, a rectangular loop laid on a slope with a conductive cubic body, and a complex-shaped loop on a real-life topography. The results of this FETD solver agreed well with the ones evaluated by the analytic methods for the first three examples, and with a frequency-domain FE solver combined with a cosine transform for the last two examples.

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