Acceleration techniques for decoupling algorithms in semiconductor simulation

We propose three techniques for accelerating the nonlinear block Gauss-Seidel algorithm for steady state semiconductor simulation: a second order stationary method, a Chebyshev acceleration and a nonlinear version of the generalized minimal residual algorithm (GMRES.) The parameters for the second order stationary method and the Chebyshev acceleration are obtained from the spectrum of the derivative of the fixed point mapping T defining the nonlinear algorithm. This spectrum is approximated by a matrix-free Arnoldi technique. The numerical results reported agree well with theoretical predictions. In particular, the nonlinear version of GMRES is found to be considerably more effective in accelerating the nonlinear map than the two second order recurrences. 36 refs., 3 figs., 1 tab.