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Iterative leap-field domain decomposition method: a domain decomposition finite element algorithm for 3D electromagnetic boundary value problems

The authors introduce the iterative leap-field domain decomposition method that is tailored to the finite element method, by combining the concept of domain decomposition and the Huygens' Principle. In this method, a large-scale electromagnetic boundary value problem is partitioned into a number of suitably-defined 'small' and manageable subproblems whose solutions are assembled to obtain the global solution. The main idea of the method is the iterative application of the Huygens' Principle to the fields radiated by the equivalent currents calculated in each iteration. In the context of the electromagnetic scattering, the method can be applied to cases involving multiple objects, as well as to a 'single' challenging object in a straightforward manner via the locally conformal perfectly matched layer technique. The most attractive feature of the method is the considerable reduction in the memory requirements and computation time. It is observed that convergence is achieved after a few iterations and computation time may further be reduced via parallel processing techniques. After developing the analytical background of this method, we present some numerical results related to the three-dimensional electromagnetic scattering problems.