  Recent developments for mathematical modeling and numerical simulation of
biomolecular systems raise new demands for qualified, stable, and efficient
surface meshing, especially in implicit-solvent modeling. In our former work,
we have developed an algorithm for manifold triangular meshing for large
Gaussian molecular surfaces, TMSmesh. In this paper, we present new algorithms
to greatly improve the meshing efficiency and qualities, and implement 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 are approximated by 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. The result
surface meshes are manifolds and can be directly used in boundary element
method (BEM) and finite element method (FEM) simulation. The binary version of
TMSmesh 2.0 is downloadable at the web page
http://lsec.cc.ac.cn/~lubz/Meshing.html.
