Application of Sobolev gradient method to Poisson-Boltzmann system

DOI10.1016/j.jcp.2010.04.017zbMath1194.82105OpenAlexW2037077117MaRDI QIDQ983028

Abdul Majid, Sultan Sial

Publication date: 28 July 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.04.017

zbMATH Keywords

Sobolev gradientsteepest descentfinite differencePoisson-Boltzmannfull approximation scheme (FAS) multigrid

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Statistical mechanics of semiconductors (82D37) Preconditioners for iterative methods (65F08)

Related Items (9)

Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradients ⋮ Optical tomography reconstruction algorithm with the finite element method: an optimal approach with regularization tools ⋮ Single-iteration Sobolev descent for linear initial value problems ⋮ A gradient based numerical approach to simulate elastic rod ⋮ A link between the steepest descent method and fixed-point iterations ⋮ Numerical solution of Burgers equation by the Sobolev gradient method ⋮ Numerical solutions of singularly perturbed reaction diffusion equation with Sobolev gradients ⋮ Space-dependent Sobolev gradients as a regularization for inverse radiative transfer problems ⋮ An accelerated Sobolev gradient method for unconstrained optimization problems based on variable inner products

Cites Work

• Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals
• Energy minimization related to the nonlinear Schrödinger equation
• Energy minimization using Sobolev gradients: application to phase separation and ordering.
• Accurate evaluation of electrostatics for macromolecules in solution
• Sobolev preconditioning for the Poisson-Boltzmann equation
• Constructing fair curves and surfaces with a Sobolev gradient method
• A Multigrid Tutorial, Second Edition
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