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

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.