On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics
type: Item
instance of: scholarly article
title: On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics
zbMATH Open document ID: 1383.78036
author: Weishan Deng
author: Jin Xu
author: Shan Zhao
published in: Journal of Computational and Applied Mathematics
publication date: 2017-11-03T00:00:00Z
review text: This paper is concerned with solving the Poisson-Boltzmann equation (PBE), a widely used implicit solvent model for the electrostatic analysis of solvated biomolecules. Some challenges of solving the PBE are that the equation has an exponential nonlinearity, complex interfaces between solute and solvent, and singular source terms. This paper develops a novel finite element method (FEM) in the pseudo-time framework for solving the PBE. By changing the time-independent problem into a time-dependent problem, the authors find that such a technique can completely suppress the nonlinear instability through the time splitting implementation. As for the singular charge sources, they investigate both the singular delta function method and the regularized delta function method. Using a body-fitted mesh, they find that the proposed pseudo-time FEM solvers are more accurate than existing pseudo-time finite difference solvers. Numerical results of several benchmark problems and free energy calculations of protein systems are presented to demonstrate the unconditional stability, accuracy, and robustness of the proposed PBE method.
reviewed by: Jichun Li
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35Q20
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 78A70
zbMATH DE Number: 6802843
zbMATH Keywords: Poisson-Boltzmann equation
zbMATH Keywords: regularized Poisson-Boltzmann equation
zbMATH Keywords: pseudo-time approach
zbMATH Keywords: finite element method
zbMATH Keywords: molecular surface
zbMATH Keywords: electrostatic free energy
cites work: tabipb
cites work: Geometric and potential driving formation and evolution of biomolecular surfaces
cites work: Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation
cites work: The Finite Element Approximation of the Nonlinear Poisson–Boltzmann Equation
cites work: A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation
cites work: Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
cites work: The electric potential of a macromolecule in a solvent: A fundamental approach
cites work: Biomolecular electrostatics using a fast multipole BEM on up to 512 GPUs and a billion unknowns
cites work: A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules
cites work: Q2935811
cites work: An Iterative Discontinuous Galerkin Method for Solving the Nonlinear Poisson Boltzmann Equation
cites work: SDPBS web server for calculation of electrostatics of ionic solvated biomolecules
cites work: Q3406191
cites work: Pseudo-time-coupled nonlinear models for biomolecular surface representation and solvation analysis
cites work: Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
cites work: Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation
cites work: New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics
cites work: Unconditionally stable time splitting methods for the electrostatic analysis of solvated biomolecules
cites work: High-Order Methods for Incompressible Fluid Flow
cites work: Spectral methods on triangles and other domains
cites work: Q5756148
cites work: Q4490850
cites work: Accurate evaluation of electrostatics for macromolecules in solution
cites work: TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator
cites work: A Poisson-Boltzmann equation test model for protein in spherical solute region and its applications
describes a project that uses: tabipb
describes a project that uses: MIBPB
describes a project that uses: TMSmesh
describes a project that uses: TABI
describes a project that uses: TetGen
describes a project that uses: SDPBS
MaRDI profile type: Publication
full work available at URL: j.cam.2017.09.004
OpenAlex ID: W2756016894
DOI: 10.1016/J.CAM.2017.09.004
description: scientific article; zbMATH DE number 6802843