Efficient and Qualified Mesh Generation for Gaussian Molecular Surface Using Adaptive Partition and Piecewise Polynomial Approximation
Tiantian Liu, Minxin Chen, Benzhuo Lu · SIAM Journal on Scientific Computing · 2018
Recent developments for mathematical modeling and numerical simulation of bio-molecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling [B. Z. Lu et al., Commun. Comput. Phys., 3 (2008), pp. 973--1009]. In our former work, we have developed an algorithm for manifold triangular meshing for large Gaussian molecular surfaces, TMSmesh [M. Chen and B. Lu, J. Chem. Theory Comput., 7 (2011), pp. 203--212; M. Chen, B. Tu, and B. Lu, J. Molecular Graphics Model., 38 (2012), pp. 411--418]. In this paper, we present new algorithms to greatly improve the meshing efficiency and qualities, and implement them into a new program version, TMSmesh 2.0. In TMSmesh 2.0, in the first step, a new adaptive partition and estimation algorithm is proposed to locate the cubes in which the surface is approximated by a piecewise trilinear surface with controllable precision. Then, the piecewise trilinear surface is divided into single valued pieces by tracing along the fold curves, which ensures that the generated surface meshes are manifolds. Numerical test results show that TMSmesh 2.0 is capable of handling arbitrary sizes of molecules and achieves ten to hundreds of times speedup over the previous algorithm. In all of our extensively tested molecules, the resulting surface meshes are all manifolds and can be used in boundary element method (BEM) and finite element method (FEM) simulation. The binary version of TMSmesh 2.0 is downloadable from the web page http://lsec.cc.ac.cn/~lubz/Meshing.html.