Accelerating the transient simulation of semiconductor devices using filter-bank transforms

Using fully or semi-implicit schemes to solve hydrodynamic transport equations is very suitable and efficient for transient simulations of semiconductor devices. But, using these techniques leads to a large system of linear equations. Here for the first time, a preconditioning method based on the filter-bank and wavelet transforms is used to facilitate the iterative solution of this system. As the first step in the performance investigation of this preconditioner in the simulation of semiconductor devices, we apply it to the modified Poisson's equation in drift-diffusion model. Numerical results show that the condition number are significantly reduced and convergence rate is increased. The most important advantage of this preconditioner rather than the other preconditioners is its low computational complexity which can be reduced to O(N).