The stationary semiconductor device equations
The stationary semiconductor device equations
On the effectiveness of Gummel's method
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
Two-dimensional exponential fitting and applications to drift-diffusion models
SIAM Journal on Numerical Analysis
ACM Transactions on Mathematical Software (TOMS)
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations
Mathematics of Computation
On Weak Residual Error Estimation
SIAM Journal on Scientific Computing
Object-oriented programming of adaptive finite element and finite volume methods
Applied Numerical Mathematics
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
A quantum corrected energy-transport model for nanoscale semiconductor devices
Journal of Computational Physics
An iterative method for finite-element solutions of the nonlinear Poisson-Boltzmann equation
ICCOMP'07 Proceedings of the 11th WSEAS International Conference on Computers
An accelerated monotone iterative method for the quantum-corrected energy transport model
Journal of Computational Physics
An iterative method for finite-element solutions of the nonlinear Poisson-Boltzmann equation
WSEAS Transactions on Computers
Nonstationary monotone iterative methods for nonlinear partial differential equations
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Hi-index | 7.30 |
Picard, Gauss-Seidel, and Jacobi monotone iterative methods are presented and analyzed for the adaptive finite element solution of semiconductor equations in terms of the Slotboom variables. The adaptive meshes are generated by the 1-irregular mesh refinement scheme. Based on these unstructured meshes and a corresponding modification of the Scharfetter-Gummel discretization scheme, it is shown that the resulting finite element stiffness matrix is an M-matrix which together with the Shockley-Read-Hall model for the generation-recombination rate leads to an existence-uniqueness-comparison theorem with simple upper and lower solutions as initial iterates. Numerical results of simulations on a MOSFET device model are given to illustrate the accuracy and efficiency of the adaptive and monotone properties of the present methods.