Adaptive Goal-Oriented Solver for the Linearized Poisson- Boltzmann Equation

An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules is developed and verified. The development is based on a derivation of a goal-oriented a posteriori error estimates for the electrostatic coupling. These estimates involve the consideration of the primal and adjoint problems for the electrostatic potential of the system. The accuracy of this solver 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. All the numerical experiments are repeated by using the well known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver