High‐convergence matrix‐solving scheme for device simulator
Shigeo Satou, Kunio Hane, Tokio Suzuki · Electronics and Communications in Japan (Part II Electronics) · 1988
Abstract This paper proposes pre‐processing and matrix computation to improve the convergence, accuracy and computation speed required in the device simulator. In the pre‐conditioning, a method to increase the number of elements and Gustafsson's modification are employed. The result of application indicated that the element‐increasing method is more effective. In the solution of the problem represented by a symmetrical matrix derived from Poisson's equation, the element‐increasing incomplete Cholesky decomposition conjugate complex gradient method (ICCG (2, 4)) is seen to be suitable. Three methods to solve the problem represented by an asymmetrical matrix, which is derived from the current continuity, are examined; the ORTHOMIN method; the bi‐conjugate gradient method; and the CG‐square (CGS) method. From the viewpoint of the convergence and the computation time, the element‐increasing incomplete LU‐decomposition CGS method (ILUCGS (2, 4)) is seen to be the best. It is demonstrated that by those matrix manipulations, the convergence of the device simulator is improved, and a solution with a satisfactory accuracy is obtained in a short computation time.