Related papers: Solution decomposition for the nonlinear Poisson-B…
We propose an edge averaged finite element(EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of the computed charged density functions and temperature function. Also…
This paper presents a numerical method for variable coefficient elliptic PDEs with mostly smooth solutions on two dimensional domains. The PDE is discretized via a multi-domain spectral collocation method of high local order (order 30 and…
Three analytic results are proposed for a linear form of the modified Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is also made with the mean spherical approximation results. The linear theories predict a…
In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…
Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic…
The energy functional, the governing partial differential equation(s) (PDE), and the boundary conditions need to be consistent with each other in a modeling system. In electrolyte solution study, people usually use a free energy form of an…
Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
Porous electrodes are widely used in electrochemical systems, where accurately determining electric potentials, particularly overpotentials, is essential for understanding electrode behavior. At the macroscopic scale, porous electrodes are…
In this paper, we present a parallel higher-order boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov…
The Poisson-Boltzmann (PB) model governs the electrostatics of solvated biomolecules, i.e., potential, field, energy, and force. These quantities can provide useful information about protein properties, functions, and dynamics. By…
We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized Poisson Boltzmann equation, for molecules represented as non-overlapping spherical cavities.…
The linear Boltzmann model for proton beams is a six-dimensional partial differential equation (PDE). We propose a deterministic solver for the linear Boltzmann model based on scattering decomposition and depth-splitting methods. The main…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…
In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
We present a soft-potential-enhanced Poisson-Boltzmann (SPB) theory to efficiently capture ion distributions and electrostatic potential around rodlike charged macromolecules. The SPB model is calibrated with a coarse-grained particle-based…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…