Monotone iterative methods for the adaptive finite element solution of semiconductor equations
Explore this paper's citation graph
Summary
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.
- Type
- article
- Published
- 2003-10-15
- Cited by
- 15
- References
- 42
- Access
- Open access
- OpenAlex
- https://openalex.org/W1967010280
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:55532621
Keywords
Mathematics, Finite element method, Discretization, Iterated function, Iterative method
References
- Topics in stability and bifurcation theory
- Analysis and simulation of semiconductor devices
- Nonlinear parabolic and elliptic equations
- Boundary Element Techniques in Engineering
- A self-consistent iterative scheme for one-dimensional steady state transistor calculations
- A new parallel adaptive finite volume method for the numerical simulation of semiconductor devices
- Toward a universal h-p adaptive finite element strategy
- Numerical methods for semiconductor device simulation
- Some a posteriori error estimators for elliptic partial differential equations
- Two-dimensional semiconductor device analysis based on new finite-element discretization employing the S-G scheme
- Supersolutions, monotone iterations, and stability
- Mildly nonlinear elliptic partial differential equations and their numerical solutoin. II
- A hybrid central difference scheme for solid-state device simulation
- Object-oriented programming of adaptive finite element and finite volume methods
- FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
- The Stationary Semiconductor Device Equations.
- Iterative scheme for computer simulation of semiconductor devices
- Monotone iterative methods for nonlinear equations involving a noninvertible linear part
- Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem
- On Weak Residual Error Estimation
Cited by
- Some parallel linear and nonlinear schwarz methods with applications in computational fluid dynamics
- An iterative method for finite-element solutions of the nonlinear Poisson-Boltzmann equation
- Block Monotone Iterative Method for Semilinear Parabolic Equations with Nonlinear Boundary Conditions
- An accelerated monotone iterative method for the quantum-corrected energy transport model
- A quantum corrected energy-transport model for nanoscale semiconductor devices
- Nonstationary monotone iterative methods for nonlinear partial differential equations
- Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations
- A posteriori error control in numerical simulations of semiconductor nanodevices
- Electron analysis of a deep sub-micrometer MOSFET device based on spectral element method
- A Fractional Drift Diffusion Model for Organic Semiconductor Devices
- New Irregular Mesh Technique Used in Three-Dimensional Simulation of Relaxation Semiconductors
- New Contribution to the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems
- Scalable Recovery-based Adaptation on Quadtree Meshes for Advection-Diffusion-Reaction Problems
- A comparison of formulations and non-linear solvers for computational modelling of semiconductor devices
- Parallel Implementation of Three-dimensional Poisson-Boltzmann Equation Solver Using Finite Element Method with Adaptive Mesh Refinement
Related papers
- Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality
- Beam on Elastic Foundation Finite Element
- The New Finite Element Method on Potential Energy Principle by Base Forces
- An a priori indicator of finite element quality based on the condition number of the stiffness matrix
- Evaluation of stiffness matrix in finite element analysis using element edge method for the 8-node brick element
- Structures: Matrix and Finite Element