TMSmesh: A Robust Method for Molecular Surface Mesh Generation Using a Trace Technique. Qualified, stable, and efficient molecular surface meshing appears to be necessitated by recent developments for realistic mathematical modeling and numerical simulation of biomolecules, especially in implicit solvent modeling (e.g., see a review in B. Z. Lu et al. Commun. Comput. Phys. 2008, 3, 973−1009). In this paper, we present a new method: tracing molecular surface for meshing (TMSmesh) the Gaussian surface of biomolecules. 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. Moreover, the meshes generated by TMSmesh are successfully tested in boundary element solutions of the Poisson−Boltzmann equation, which directly gives rise to a route to simulate electrostatic solvation of large-scale molecular systems. The binary version of TMSmesh and a set of representative PQR benchmark molecules are downloadable at our Web page∼lubz/Meshing.html.

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  1. Wang, Qin; Ma, Zhaocan; Bai, Shiyang; Zhang, Linbo; Lu, Benzhuo; Li, Hongliang: Research on parallel finite element methods for the drift-diffusion model in semiconductor device simulations (2020)
  2. Xie, Dexuan; Lu, Benzhuo: An effective finite element iterative solver for a Poisson-Nernst-Planck ion channel model with periodic boundary conditions (2020)
  3. Yang, Ying; Tang, Ming; Liu, Chun; Lu, Benzhuo; Zhong, Liuqiang: Superconvergent gradient recovery for nonlinear Poisson-Nernst-Planck equations with applications to the ion channel problem (2020)
  4. Zhang, Qianru; Gui, Sheng; Li, Hongliang; Lu, Benzhuo: Model reduction-based initialization methods for solving the Poisson-Nernst-Planck equations in three-dimensional ion channel simulations (2020)
  5. Hazra, Tania; Ullah, Sheik Ahmed; Wang, Siwen; Alexov, Emil; Zhao, Shan: A super-Gaussian Poisson-Boltzmann model for electrostatic free energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states (2019)
  6. Pérez-Arancibia, Carlos; Turc, Catalin; Faria, Luiz: Planewave density interpolation methods for 3D Helmholtz boundary integral equations (2019)
  7. Zhang, Bo; Debuhr, Jackson; Niedzielski, Drake; Mayolo, Silvio; Lu, Benzhuo; Sterling, Thomas: DASHMM accelerated adaptive fast multipole Poisson-Boltzmann solver on distributed memory architecture (2019)
  8. Chen, Jiahui; Geng, Weihua: On preconditioning the treecode-accelerated boundary integral (TABI) Poisson-Boltzmann solver (2018)
  9. Deng, Weishan; Xu, Jin; Zhao, Shan: On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics (2018)
  10. Liu, Tiantian; Chen, Minxin; Lu, Benzhuo: Efficient and qualified mesh generation for Gaussian molecular surface using adaptive partition and piecewise polynomial approximation (2018)
  11. Mu, Lin; Xia, Kelin; Wei, Guowei: Geometric and electrostatic modeling using molecular rigidity functions (2017)
  12. Qiao, Yu; Liu, Xuejiao; Chen, Minxin; Lu, Benzhuo: A local approximation of fundamental measure theory incorporated into three dimensional Poisson-Nernst-Planck equations to account for hard sphere repulsion among ions (2016)
  13. Xie, Yan; Liu, Tiantian; Tu, Bin; Lu, Benzhuo; Zhang, Linbo: Automated parallel and body-fitted mesh generation in finite element simulation of macromolecular systems (2016)
  14. Tu, Bin; Xie, Yan; Zhang, Linbo; Lu, Benzhuo: Stabilized finite element methods to simulate the conductances of ion channels (2015)
  15. Zhang, Bo; Peng, Bo; Huang, Jingfang; Pitsianis, Nikos P.; Sun, Xiaobai; Lu, Benzhuo: Parallel AFMPB solver with automatic surface meshing for calculation of molecular solvation free energy (2015)
  16. Geng, Weihua: Parallel higher-order boundary integral electrostatics computation on molecular surfaces with curved triangulation (2013)
  17. Geng, Weihua; Jacob, Ferosh: A GPU-accelerated direct-sum boundary integral Poisson-Boltzmann solver (2013)
  18. Geng, Weihua; Krasny, Robert: A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules (2013)
  19. Li, Chuan; Li, Lin; Petukh, Marharyta; Alexov, Emil: Progress in developing Poisson-Boltzmann equation solvers (2013)
  20. Lu, Benzhuo: Finite element modeling of biomolecular systems in ionic solution (2013)

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