A parallel block iterative method for the hydrodynamic device model

Block iterative methods are applied to hydrodynamic simulations of a one-dimensional (1-D) submicrometer semiconductor device. We show that block successive underrelaxation (SUR) converges with a fixed relaxation factor w = 0.13 for simulations at 300 K and w = 0.04 at 77 K . To demonstrate the robustness of the block iterative method, we present numerical simulations of a steady-state electron shock wave in Si at 300 K for a 0.1-pm channel and at 77 K for a 1.0-pm channel. The block SUR method is parallelizable if each diagonal block solve can be done efficiently in parallel. Using chaotic relaxation and the preconditioned conjugate gradient method for the parallel diagonal block solves, we obtain a parallel speed up of approximately 2.5 on 10 processors of a Butterfly GP-1000. The 1-D simulations serve as a numerical laboratory for developing methods that will be essential for computational efficiency in two-dimensional (2-D) problems.