Efficient and Qualified Mesh Generation for Gaussian Molecular Surface Using Piecewise Trilinear Polynomial Approximation

TL;DR

This paper introduces TMSmesh 2.0, an improved algorithm for generating high-quality, manifold surface meshes of Gaussian molecular surfaces efficiently, enabling faster biomolecular simulations.

Contribution

The paper presents new adaptive partitioning and trilinear approximation algorithms that significantly enhance meshing efficiency and quality for large biomolecular surfaces.

Findings

Achieves 10-100x speedup over previous methods.

Produces manifold surface meshes suitable for BEM and FEM.

Handles arbitrary molecule sizes effectively.

Abstract

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.