An automatic three-dimensional finite element mesh generation system for the Poisson-Boltzmann equation

We present an automatic three-dimensional mesh generation system for the solution of the Poisson-Boltzmann equation using a finite element discretization. The different algorithms presented allow the construction of a tetrahedral mesh using a predetermined spatial distribution of vertices adapted to the geometry of the dielectric continuum solvent model. A constrained mesh generation strategy, based on Bowyer's algorithm, is used to construct the tetrahedral elements incrementally and embed the Richards surface of the molecule into the mesh as a set of triangular faces. A direct mesh construction algorithm is then used to refine the existing mesh in the neighborhood of the dielectric interface. This will allow an accurate calculation of the induced polarization charge to be carried out while maintaining a sparse grid structure in the rest of the computational space. The inclusion of an ionic boundary at some finite distance from the dielectric interface can be automatically achieved as the grid point distribution outside the solute molecule is constructed using a set of surfaces topologically equivalent to this boundary. The meshes obtained by applying the algorithm to real molecular geometries are described. (C) 1997 John Wiley & Sons, Inc.