Surface Triangular Mesh and Volume Tetrahedral Mesh Generations for Biomolecular Modeling
Qualified, stable and efficient molecular surface/volume meshing appears to be necessitated by recent developments for realistic mathematical modeling and numerical simulation of biomolecules, especially in implicit solvent modeling. The chapter first describes a tool, TMSmesh, for surface meshing through tracing a molecular Gaussian surface. The method computes the surface points by solving a nonlinear equation directly, polygonizes by connecting surface points through a trace technique, and finally outputs a triangulated mesh. TMSmesh has a linear complexity with respect to the number of atoms and is shown to be capable of handling molecules consisting of more than one million atoms, which is usually difficult for the existing methods for surface generation used in molecular visualization and geometry analysis. Then, based on the surface mesh, a tool chain is built up to generate high-quality biomolecular volume tetrahedral mesh. The performances of these meshing tools are analyzed, and the surface/volume meshes are shown to be applicable to boundary element/finite element types of simulations of Poisson–Boltzmann electrostatics.
KeywordsSurface Mesh Molecular Surface Tetrahedral Mesh Mesh Quality Tool Chain
M.X. Chen was supported in part by the China NSF (NSFC11001062) and Collegiate NSF of Jiangsu Province (No. 11KJB110010). B. Tu and B.Z. Lu was supported by the Chinese Academy of Sciences, the State Key Laboratory of Scientific/Engineering Computing, National Center for Mathematics and Interdisciplinary Sciences, and the China NSF (NSFC10971218).
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