Circuit module placement method based on physical model

This paper proposes an efficient circuit module placement based on a force model. It is known that the module placement based on the force model arrives at a placement relatively close to the optimum. However, in the traditional method, a repulsive force is employed. As a result, the equation be comes nonlinear with a large number of variables, which is not easy to handle. First, this paper shows a simplification by replacing the forementioned problem by a nonlinear equation with a single variable. Then the module placement based on the foregoing formulation is proposed. Discussions are made on the size of the module, the case of multi-terminal nets and the optimality of the obtained placement. Finally, a result of application to the placement design of the gate array is presented, indicating the use fulness of the proposed method. the features of the method are that the solution of the nonlinear equation can easily be determined, and the sparse matrix technique can be applied. Consequently, it is applicable to the placement design of a large-scale circuit with more than 1000 modules.