Linear scaling computation of forces for the domain-decomposition linear Poisson--Boltzmann method

The Linearized Poisson–Boltzmann (LPB) equation is a popular and widely accepted model for accounting solvent effects in computational (bio-) chemistry. In the present article we derive the analytical forces of the domain-decomposition-based ddLPB-method with vdW or SAS surface. We present an efficient strategy to compute the forces and its implementation, allowing linear scaling of the method with respect to the number of atoms using the fast multipole method (FMM). Numerical tests illustrates the accuracy of the computation of the analytical forces and compares efficiency with other available methods.