The exploitation of geometrical symmetry in 3-D Eddy-currents computation

The incidence of symmetry in the computation of network impedances has been thoroughly studied since the seminal work of Fortescue [2]. See e.g [3]. But as regards field computations, the same question, namely "how to take advantage of geometrical symmetry to reduce the size of computations" seems relatively untouched, though the basic theory is the same. The problem is especially interesting when the source field does not share the symmetry of the system of conductors, the analog in the context of field calculations of the classical question of unbalanced regime in polyphase networks. We show that, by making use of the symmetry, one can reduce the original problem to a series of sub-problems on a space domain of reduced size, with substantial cost savings. We especially address here the question of finding the right boundary conditions for these subproblems, a non trivial matter when the symmetry group is not commutative.