A Domain Decomposition Method for the Poisson-Boltzmann Solvation Models
This method addresses the need for efficient and accurate solvation models in computational chemistry, particularly for coupling with quantum mechanical descriptions.
The paper proposes a domain decomposition method (ddLPB) for solving the linear Poisson-Boltzmann equation in computational chemistry, achieving exponential convergence of solvation energy with respect to degrees of freedom, enabling accurate coupling with quantum mechanical solute models.
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 $\mathbb R^3$ 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.