基于分段三线性多项式逼近的高斯分子表面高效高质量网格生成
Efficient and Qualified Mesh Generation for Gaussian Molecular Surface Using Piecewise Trilinear Polynomial Approximation
AI总结：
本文提出TMSmesh 2.0算法，通过分段三线性表面逼近提升网格生成效率和质量，实现十至百倍速度提升，生成的网格可直接用于边界元法和有限元法模拟。
摘要：
近期数学建模和生物分子系统数值模拟的发展对高质量、稳定和高效的表面网格生成提出了新要求，特别是在隐式溶剂建模中。在前人工作中，我们开发了用于大尺寸高斯分子表面的流形三角网格生成算法TMSmesh。本文提出新的算法大幅提升了网格生成效率和质量，并在新版本TMSmesh 2.0中实现。在TMSmesh 2.0中，首先提出新的自适应分区和估计算法，定位用分段三线性表面近似且具有可控精度的立方体。然后通过追踪折叠曲线将分段三线性表面分成单值部分，确保生成的表面网格为流形。数值测试结果表明，TMSmesh 2.0能够处理任意大小的分子，并在之前算法基础上实现十至百倍的速度提升。生成的表面网格为流形，可直接用于边界元法（BEM）和有限元法（FEM）模拟。TMSmesh 2.0的二进制版本可在网页http://lsec.cc.ac.cn/~lubz/Meshing.html下载。
英文摘要：
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.
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