Numerical Computing of Molecular Electrostatics through Boundary Integral Equations

In continuum approaches to molecular electrostatics, boundary element method (BEM) can provide accurate solutions to the Poisson-Boltzmann equation. However, the numerical aspects of this method are fraught with di culties. We describe our approach applying an alpha shape-based method to generate a high quality mesh, which represents the shape and topology of the molecule precisely. We also describe the analytical method to map points from the planar mesh to their exact locations on the surface of the molecule. We demonstrate that derivative boundary integral formulation has numerical advantages over the nonderivative formulation: the well-conditioned in uence matrix can be maintained without deteriorating condition number when the number of the mesh elements scale up. Singular integrand kernels are characteristics of the BEM. Their accurate integration is an important issue. We describe variable transformations that allow accurate numerical integraton, the only plausible integral