Finite-volume simulations of Maxwell's equations on unstructured grids
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Herein a fully parallel, upwind and flux-split Finite-Volume Time-Domain (FVTD) numerical engine for solving Maxwell's Equations on unstructured grids is developed. The required background theory for solving Maxwell's Equations using FVTD is given in sufficient detail, including a description of both the temporal and spatial approximations used. The details of the local-time stepping strategy of Fumeaux et al. is included. A global mesh-truncation scheme using field integration over a Huygens' surface is also presented. The capabilities of the FVTD algorithm are augmented with thin-wire and subcell circuit models that permit very flexible and accurate simulations of circuit-driven wire structures. Numerical and experimental validation shows that the proposed models have a wide-range of applications. Specifically, it appears that the thin-wire and subcell circuit models may be very well suited to the simulation of radio-frequency coils used in magnetic resonance imaging systems. A parallelization scheme for the volumetric field solver, combined with the local-time stepping, global mesh-truncation and subcell models is developed that theoretically provides both linear time- and memory scaling in a distributed parallel environment. Finally, the FVTD code is converted to the frequency domain and the possibility of using different flux-reconstruction schemes to improve the iterative convergence of the Finite-Volume Frequency-Domain algorithm is investigated.