ARGOS: An adaptive refinement goal‐oriented solver for the linearized Poisson–Boltzmann equation

Abstract

An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules in a solvent environment is developed and tested. At the heart of the solver is a goal‐oriented a posteriori error estimate for the electrostatic coupling, derived and implemented in the present work, that gives rise to an orders of magnitude improved precision and a shorter computational time as compared to standard finite difference solvers. The accuracy of the new solver ARGOS is evaluated by numerical experiments on a series of problems with analytically known solutions. In addition, the solver is used to calculate electrostatic couplings between two chromophores, linked to polyproline helices of different lengths and between the spike protein of SARS‐CoV‐2 and the ACE2 receptor. All the calculations are repeated by using the well‐known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver.

Coupling finite and boundary element methods to solve the Poisson–Boltzmann equation for electrostatics in molecular solvation

“…The molecular surface can be defined in various ways. 6 The PBE has been solved numerically with finite difference, [7][8][9][10] finite element, [11][12][13] boundary element, [14][15][16][17][18][19] and analytic [20][21][22][23][24] methods. In particular, the boundary element method (BEM) has proven to be very efficient for high-accuracy calculations, 18,19 mainly due to the precise description of the molecular surface and point charges.…”

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson–Boltzmann Framework: An Analytical Treatment

“…This, however, does not diminish the importance of studying the behavior of the LPBE also in the case of highly charged objects: their electrostatics may still be correctly described at sufficiently long distances (as compared to the Debye length) by the usual DH approximation provided that the sources of the electric field are properly renormalized. − (See also the recent ref for additional comments concerning the ranges of applicability of the DH theory.) This once again emphasizes the importance of a thorough study of the DH approximations, both theoretically and numerically, and justifies the constant stream of works related to the LPBE (see recent refs , , and − , and references therein).…”