A1 Journal article (refereed)
Reliable Computer Simulation Methods for electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation (2020)

Kraus, J., Nakov, S., & Repin, S. (2020). Reliable Computer Simulation Methods for electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation. Computational Methods in Applied Mathematics, 20(4), 643-676. https://doi.org/10.1515/cmam-2020-0022

JYU authors or editors

Publication details

All authors or editors: Kraus, Johannes; Nakov, Svetoslav; Repin, Sergey

Journal or series: Computational Methods in Applied Mathematics

ISSN: 1609-4840

eISSN: 1609-9389

Publication year: 2020

Publication date: 27/09/2020

Volume: 20

Issue number: 4

Pages range: 643-676

Publisher: Walter de Gruyter GmbH

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1515/cmam-2020-0022

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1805.11441

Abstract

The paper is concerned with the reliable numerical solution of a class of nonlinear interface problems governed by the Poisson–Boltzmann equation. Arising in electrostatic biomolecular models these problems typically contain measure-type source terms and their solution often exposes drastically different behaviour in different subdomains. The interface conditions reflect the requirement that the potential and its normal derivative must be continuous. In the first part of the paper, we discuss an appropriate weak formulation of the problem that guarantees existence and uniqueness of the generalized solution. In the context of the considered class of nonlinear equations, this question is not trivial and requires additional analysis, which is based on a special splitting of the problem into simpler subproblems whose weak solutions can be defined in standard Sobolev spaces. This splitting also suggests a rational numerical solution strategy and a way of deriving fully guaranteed error bounds. These bounds (error majorants) are derived for each subproblem separately and, finally, yield a fully computable majorant of the difference between the exact solution of the original problem and any energy-type approximation of it.

Keywords: electrochemistry; molecular dynamics; biomolecules; simulation; partial differential equations; numerical analysis

Free keywords: electrostatic biomolecular models; nonlinear elliptic interface problems; measure right-hand side; Poisson–Boltzmann equation; reliable computer simulation; adaptive methods; a posteriori error estimates

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 1