A Domain Decomposition Method for the Poisson--Boltzmann Solvation Models

Abstract

In this paper, a domain decomposition method for the Poisson-Boltzmann (PB) solvation model that is widely used in computational chemistry is proposed. This method, called ddLPB for short, solves the linear Poisson-Boltzmann (LPB) equation defined in R 3 using the van der Waals cavity as the solute cavity. The Schwarz domain decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in balls. A series of numerical experiments is presented to test the robustness and the efficiency of this method including the comparisons with some existing methods. We observe exponential convergence of the solvation energy with respect to the number of degrees of freedom which allows this method to reach the required level of accuracy when coupling with quantum mechanical descriptions of the solute.

How to make continuum solvation incredibly fast in a few simple steps: A practical guide to the domain decomposition paradigm for the conductor‐like screening model

“…[29] The domain decomposition paradigm has recently been extended [19,20] to the Integral Equation Formalism-Polarizable Continuum Model (IEF-PCM) [30] and to the solution of the linearized Poisson-Boltzmann equation. [31] Extensions of the domain decomposition paradigm to the Solvent Excluded Surface (SES) type of molecular surface [32,33] have also been developed. [34] The extension of ddCOSMO and its generalizations to other molecular properties is being actively investigated in our groups.…”

“…The domain decomposition paradigm has recently been extended to the Integral Equation Formalism‐Polarizable Continuum Model (IEF‐PCM) and to the solution of the linearized Poisson‐Boltzmann equation . Extensions of the domain decomposition paradigm to the Solvent Excluded Surface (SES) type of molecular surface have also been developed…”

“…Computation of the forces -ddCOSMO exclusive terms. These contributions stem from the derivatives of the ddCOSMO L matrix (seeEquation 14) and from the derivatives of the characteristic function (see Equation31.). The FORCES_DD subroutine from the ddCOSMO package takes care of assembling these terms.…”

Computation of forces arising from the linear Poisson--Boltzmann method in the domain-decomposition paradigm

“…The latter takes the majority of cost but can be further accelerated using for example the fast multipole method (FMM). Numerical implementations show that the ddLPB solver is very efficient even without acceleration techniques (see [QSM19] for details) and its FMM-acceleration is ongoing work in progress but not within the scope of this article. The focus of this work is to develop the framework of the computation of first derivatives and the forces for the ddLPB method, the FMM-acceleration is a subsequent step.…”

A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

“…An alternative approach is to reformulate the PB equation as a boundary integral equation and use the boundary elements to discretize the molecular surface, e.g. [25][26][27][28][29][30][31][32][33]. Besides the reduction from three dimensional space to the two dimensional molecular boundary, this approach has the advantage that singular charges, interface conditions, and far-field condition are incorporated analytically in the formulation, and hence do not impose additional approximation errors.…”