The modeling of quasi-static optimization problems often involves divergence-free surface current densities. In this paper, a novel technique to implement these currents by using the boundary element method framework is presented. A locally-based characterization of the current density is employed, to render a fully geometry-independent formulation, so that it can be applied to arbitrary shapes. To illustrate the versatility of this approach, we employ it for the design of gradient coils for MRI, providing a solid mathematical framework for this type of problem.
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