About the Solution of the Three-dimensional Semiconductor Device Equations on Vector-concurrent Computers

The discretization of the semiconductor equations in three-dimensional device simulators leads to very large sparse linear systems of equations. While the solution of the Poisson equation e.g. by the conjugate gradient methodis straightforward, the iterative solution of the carrier continuity equations is nontrivial due to both the non-symmetry and the poor conditioning of the coefficient matrices. As a consequence we have investigated conjugate gradient-like iterative methods such as conjugate gradients applied to the normal equations, a symmetrized conjugate gradient method, ORTHOMIN, GMRES and three squared hiconjugate gradient algorithms. All these methods were implemented in conjunction with incomplete factorization preconditioners, since the large condition number of the coefficient matrices makes preconditioning indispensable. We demonstrate the effectiveness of our implementation on vector and vector-concurrent supercomputers, such as the Fujitsu VP200, Cray-2 and on minisupercomputers, such as the ALLIANT /FX40 and VAX 6260.