Parallel Adaptive Finite Element Algorithms for Solving the Coupled Electro-diffusion Equations

DOI10.2478/mlbmb-2013-0005zbMath1276.35143OpenAlexW2139119394MaRDI QIDQ2863927

Jie Cheng, Benzhuo Lu, Yan Xie, Linbo Zhang

Publication date: 5 December 2013

Published in: Computational and Mathematical Biophysics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/mlbmb-2013-0005

zbMATH Keywords

parallel processingadaptive finite element methodPoisson-Nernst-Planck equationsDIISslotboom variablessoftware package PHG

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Related Items (8)

A local approximation of fundamental measure theory incorporated into three dimensional Poisson-Nernst-Planck equations to account for hard sphere repulsion among ions ⋮ Stabilized finite element methods to simulate the conductances of ion channels ⋮ A weak Galerkin finite element method for time-dependent Poisson-Nernst-Planck equations ⋮ Adaptive finite element approximation for steady-state Poisson-Nernst-Planck equations ⋮ 稳态Poisson-Nernst-Planck方程的后验误差估计 ⋮ Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations ⋮ Residual type a posteriori error estimates for the time-dependent Poisson-Nernst-Planck equations ⋮ Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes

Uses Software

• TetGen
• ParaView
• FEtk
• PHG
• TMSmesh
• TransforMesh

Cites Work

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• Second-order Poisson-Nernst-Planck solver for ion transport
• An efficient, reliable and robust error estimator for elliptic problems in \(\mathbb R^3\)
• The adaptive immersed interface finite element method for elliptic and Maxwell interface problems
• Local adaptive mesh refinement for shock hydrodynamics
• Accurate evaluation of electrostatics for macromolecules in solution
• Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes. I: Finite element solutions
• Semiconductor Device Simulation
• Numerical Methods for Semiconductor Device Simulation

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