Positivity preserving discretization of time dependent semiconductor drift-diffusion equations

DOI10.1016/j.apnum.2012.06.016zbMath1258.82009OpenAlexW2062911638MaRDI QIDQ450888

Markus Brunk, Anne Kværnø

Publication date: 26 September 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.06.016

zbMATH Keywords

mixed finite elementssplitting methoddrift-diffusion equationspositivity preservationsemiconductor model

Mathematics Subject Classification ID

Statistical mechanics of semiconductors (82D37) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (5)

A linearized local conservative mixed finite element method for Poisson-Nernst-Planck equations ⋮ A Convergent Iteration Scheme for Semiconductor/Circuit Coupled Problems ⋮ A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation ⋮ Linearized conservative finite element methods for the Nernst-Planck-Poisson equations ⋮ Numerical analysis of locally conservative weak Galerkin dual-mixed finite element method for the time-dependent Poisson-Nernst-Planck system

Uses Software

• Matlab
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

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• Gaussian elimination is not optimal
• The MATLAB ODE Suite
• Numerical Coupling of Electric Circuit Equations and Energy-Transport Models for Semiconductors
• Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques
• Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Numerical Discretization of Energy-Transport Models for Semiconductors with Nonparabolic Band Structure
• Two characterizations of inverse-positive matrices: the Hawkins-Simon condition and the Le Chatelier-Braun principle
• On a hierarchy of macroscopic models for semiconductors
• NEW MIXED FINITE ELEMENT SCHEMES FOR CURRENT CONTINUITY EQUATIONS

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