Journal of Computational and Applied Mathematics
Numerical estimates for semilinear parabolic equations
SIAM Journal on Numerical Analysis
On the effectiveness of Gummel's method
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations
Mathematics of Computation
Object-oriented programming of adaptive finite element and finite volume methods
Applied Numerical Mathematics
A monotone finite element scheme for convection-diffusion equations
Mathematics of Computation
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Monotone iterative methods for the adaptive finite element solution of semiconductor equations
Journal of Computational and Applied Mathematics
On monotone iterative methods for a nonlinear singularly perturbed reaction-diffusion problem
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A quantum corrected energy-transport model for nanoscale semiconductor devices
Journal of Computational Physics
Quantum-corrected drift-diffusion models for transport in semiconductor devices
Journal of Computational Physics
Hi-index | 7.29 |
A simple technique is given in this paper for the construction and analysis of monotone iterative methods for a class of nonlinear partial differential equations. With the help of the special nonlinear property we can construct nonstationary parameters which can speed up the iterative process in solving the nonlinear system. Picard, Gauss-Seidel, and Jacobi monotone iterative methods are presented and analyzed for the adaptive solutions. The adaptive meshes are generated by the 1-irregular mesh refinement scheme which together with the M-matrix of the finite element stiffness matrix lead to existence-uniqueness-comparison theorems with simple upper and lower solutions as initial iterates. Some numerical examples, including a test problem with known analytical solution, are presented to demonstrate the accuracy and efficiency of the adaptive and monotone properties. Numerical results of simulations on a MOSFET with the gate length down to 34 nm are also given.