Newton Solvers for Drift-Diffusion and Electrokinetic Equations

DOI10.1137/17M1146956zbMath1448.65151OpenAlexW2810086808WikidataQ129649263 ScholiaQ129649263MaRDI QIDQ4569315

Maximilian S. Metti, Arthur Bousquet, Xiaozhe Hu, Jin-Chao Xu

Publication date: 28 June 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1146956

zbMATH Keywords

stability analysisfinite elementsPoisson-Nernst-Plancknumerical solvers

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

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Uses Software

• FEniCS
• SyFi

Cites Work

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• Multigrid methods for the Stokes equations using distributive Gauss-Seidel relaxations based on the least squares commutator
• Spectral problems for non-elliptic symmetric systems with dissipative boundary conditions
• A simple preconditioner for a discontinuous Galerkin method for the Stokes problem
• Application of auxiliary space preconditioning in field-scale reservoir simulation
• A mathematical model for the hard sphere repulsion in ionic solutions
• Automated solution of differential equations by the finite element method. The FEniCS book
• Energetically stable discretizations for charge transport and electrokinetic models
• Some upwinding techniques for finite element approximations of convection-diffusion equations
• The alternate-block-factorization procedure for systems of partial differential equations
• Numerical simulation of semiconductor devices
• L\({}_{\infty}\) stability of finite element approximations to elliptic gradient equations
• Convergent discretizations for the Nernst-Planck-Poisson system
• Finite element methods for convection-diffusion problems using exponential splines on triangles
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• The finite volume Scharfetter-Gummel method for steady convection diffusion equations
• Modeling electrokinetic flows by consistent implicit incompressible smoothed particle hydrodynamics
• Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes. I: Finite element solutions
• A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
• A New Approximate Block Factorization Preconditioner for Two-Dimensional Incompressible (Reduced) Resistive MHD
• Preconditioning discretizations of systems of partial differential equations
• A Multigrid Solver based on Distributive Smoother and Residual Overweighting for Oseen Problems
• Multigrid analysis for the time dependent Stokes problem
• A triangular mixed finite element method for the stationary semiconductor device equations
• Inverse-Average-Type Finite Element Discretizations of Selfadjoint Second-Order Elliptic Problems
• Convergent finite element discretizations of the Navier-Stokes-Nernst-Planck-Poisson system
• Numerical Methods for Semiconductor Device Simulation
• Consistency of Semiconductor Modeling: An Existence/Stability Analysis for the Stationary Van Roosbroeck System
• An Observation Concerning Ritz-Galerkin Methods with Indefinite Bilinear Forms
• Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models
• A monotone finite element scheme for convection-diffusion equations
• Algebraic multigrid methods
• A Preconditioner for Generalized Saddle Point Problems
• A locally conservative LDG method for the incompressible Navier-Stokes equations
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• A Block Preconditioner for an Exact Penalty Formulation for Stationary MHD
• A multigrid method based on graph matching for convection–diffusion equations
• Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment
• Modeling and simulating asymmetrical conductance changes in gramicidin pores
• Uniform preconditioners for the time dependent Stokes problem

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