PRECONDITIONED ITERATIVE METHODS FOR SPARSE LINEAR ALGEBRA PROBLEMS ARISING IN-CIRCUIT SIMULATION

The DC operating point of a circuit may be computed by tracking the ze ro curve of an associated artificial-parameter homotopy. It is possibl e to devise homotopy algorithms that are globally convergent with prob ability one for the DC operating point problem. These algorithms requi re computing the one-dimensional kernel of the Jacobian matrix of the homotopy mapping at each step along the zero curve, and hence, the sol ution of a linear system of equations at each step. These linear syste ms are typically large, highly sparse, nonsymmetric and indefinite. Se veral iterative methods which are applicable to nonsymmetric and indef inite problems are applied to a suite of test problems derived from si mulations of actual bipolar circuits. Methods tested include Craig's m ethod, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQ R. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, inclu ding incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence s tatistics are given for each iterative method and preconditioner.