A Divergence-Free BEM Method to Model Quasi-Static Currents: Application to MRI Coil Design

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. 1. INTRODUCTION Many problems in engineering require to determine the spatial distribution of electric currents ∞owing in a conductive surface which satisfles given requirements for the flelds, electromagnetic energy, etc. they produce. The reconstruction of current distribution on the conducting surface subjected to these constraints can be seen as an inverse problem. An appropriate and realistic formulation of this type of problems is presented in this paper, by incorporating a suitable model of the current under search, in terms of the stream function, into the Boundary Element Method (BEM). The use of stream function for the characterization of surface current densities has been widely employed (1). The BEM has been proved to be an excellent tool in the solution of electromagnetic problems (2,3); and the incorporation of the stream function into a numerical computational technique, such us BEM, has also been already considered for the solution of electromagnetic inverse