Three‐dimensional electromagnetic analysis by the subspace synthesis method

Abstract

AbstractThe required computer memory capacity and the calculation time become enormous when analyzing problems for three‐dimensional electromagnetic fields by finite‐element methods. In many cases calculation is difficult even by a super‐computer. To save the required computer memory capacity and computer time, we propose a subspace synthesis method, an outline of which is as follows. First, the object space is divided into several subspaces. In each subspace we apply the finite‐element method. We formulate dispersed equations for each subspace. From these equations we derive reduced equations which relate only the unknown coefficients on connecting regions among sub‐spaces. By combining reduced equations from all subspaces, we obtain the reduced equations for the total object space. By solving them we can obtain the electromagnetic fields. In the proposed method, we execute calculations for a small subspace one at a time. Therefore the required computer memory capacity is reduced greatly from that for analyzing the object space by the direct application of the finite‐element method. The corresponding computer calculation time is also reduced. This paper shows the formulation of the subspace synthesis method, and applies it to several examples. The calculation results by the present method were compared with rigorous solutions or experimental data. The effectiveness of the proposed method was shown from these comparisons.