Polynomial Acceleration Of Gummel´s Method

We successfully employ polynomial acceleration of Gummel´s method for decoupling the equations describing steady state semiconductors. We present numerical results which demonstrate that the speed of convergence has been increased up to a factor of four. The polynomial acceleration is based on an analysis of Gummel´s method as a non linear fixed point mapping T. The accelerating polynomials are determined from the location in the complex plane of the eigenvalues of the derivative T´ of T. We present these complex eigenvalue spectra which have been obtained both computationally and theoretically. We discuss the choice of polynomials from these spectra. Moreover, we examine the implications of the nonlinearity of T for polynomial acceleration.