Title: A fast ADI algorithm for nonlinear Poisson equation in heterogeneous dielectric media

Authors: Wufeng Tian

Addresses: Department of Mathematics, University of Wisconsin-Eau Claire, Eau Claire, 54701, WI, USA

Abstract: A nonlinear Poisson equation (NPE) has been introduced to model nonlinear and nonlocal hyperpolarisation effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due to a strong nonlinearity associated with the heterogeneous dielectric media, the NPE is difficult to solve numerically for large protein systems. A new pseudo-transient continuation approach is proposed in this paper to solve the nonlinear Poisson equation efficiently and stably. An alternating direction implicit (ADI) method is developed for solving the pseudo-time dependent Poisson equation. The proposed scheme is validated by considering benchmark examples with exact solutions and by solvation analysis of real biomolecules with various sizes. Numerical results are in good agreement with the theoretical prediction, experimental measurements, and those obtained from the boundary value problem approach. Since the time stability of the proposed ADI scheme can be maintained even using very large time increments, it is efficient for electrostatic analysis involving hyperpolarisation effects.

Keywords: nonlinear Poisson equation; nonlocal dielectric media; Pseudotransient continuation approach; biological molecule; ADI; alternating direction implicit; solvation free energy; electrostatic free energy.

DOI: 10.1504/IJCSM.2021.118794

International Journal of Computing Science and Mathematics, 2021 Vol.14 No.2, pp.107 - 123

Received: 01 Aug 2019
Accepted: 27 Jan 2020
Published online: 08 Nov 2021 *

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