The electric or electronic circuits have many contact devices such as relay and switch. The contact between two nominally conducting flat surface has a lot of micro contact spots. The constriction resistance of the contact is known to determine the sum of the parallel resistance of the micro contacts and the interaction of them. The constriction resistance of two circular conducting spots was approximately formulated by Greenwood. This formulation shows that the interacted resistance of two circular spots is in inverse proportion to the distance between two conducting spots. It was known that this effect is introduced by the interaction between two conducting spots. However, the condition of interaction in the spots is not clear. Calculating the current density distribution in the spots is important to clarify the condition of interaction. The numerical analysis is very suitable to calculate the current density in the spots. In the fundamental case of the computation of the current density the boundary element method (BEM) is more efficient and accurate than that of the finite element method (FEM) because the boundary condition at the infinite is naturally satisfied and is not required a great number of the element in a wide space. In this paper the current density in the square spots is computed by the BEM. As the distance between two conducting spots becomes small, the current density in the two spots decreases. It becomes clear that the constriction resistance of conducting spots is increased by this effect. The decrease of current density by interaction is not uniformly, that at the near location to the opposite spot is larger than that at the far location in the same spot. In this paper the constriction resistance of two conducting spots is also considered. It was known that the constriction resistance of one conducting spot is not influenced by the form of spot very much. However, that of two conducting spots is not clear. The constriction resistance of two square spots is also computed by the BEM. The computed values of the constriction resistance of two square spots are compared with that of two circular spots by Greenwood's formulation and other results. As the result, it is clear that they have the considerable discrepancy. However, the trend of the variations is almost agree each other.

Simple expressions for constriction resistance of multitude conducting spots were analytically formulated by Greenwood. These expressions, however, include some approximations. Nakamura presented that the constriction resistance of one circular spot computed using the BEM is closed to Maxwell's exact value. This relative error is only e=0. 00162 [%]. In this study, the constriction resistances of two, five and ten conducting spots are computed using the boundary element method (BEM), and compared with those obtained using Greenwood's expressions. As the conducting spots move close to each other, the numerical deviations between constriction resistances computed using Greenwood's expressions and the BEM increase. As a result, mutual resistance computed by the BEM is larger than that obtained from Greenwood's expressions. The numerical deviations between the total resistances computed by Greenwood's expressions and that by the BEM are small. Hence, Greenwood's expressions are valid for the total constriction resistance calculation and can be applied to problems where only the total resistance of two contact surfaces, such as a relay and a switch, is required. However, the numerical deviations between the partial resistances computed by Greenwood's expression and that by the BEM are very large. The partial resistance calculations of multitude conducting spots are beyond the applicable range of Greenwood's expression, since Greenwood's expression for constriction resistance of two conducting spots is obtained by assuming that the conducting spots are equal size. In particular, the deviation between resistances of conducting spots, which are close to each other, is very large. In the case of partial resistances which are significant in semiconductor devices, Greenwood's expressions cannot be used with high precision.