Triangulated manifold meshing method preserving molecular surface topology.

Area of Science:

• Computational biology
• Mathematical modeling
• Surface meshing

Background:

• Generating manifold surface meshes is critical for biomolecule simulations using boundary element methods (BEM) and finite element methods (FEM).
• Existing meshing methods often produce defective surface meshes with issues like non-closed surfaces, element intersections, and missing small structures, requiring manual correction.
• These defects hinder the direct application of meshes in BEM and FEM calculations.

Purpose of the Study:

• To present an improved meshing method that generates defect-free manifold surface meshes for biomolecular Gaussian surfaces.
• To avoid mesh intersections and preserve the topology of molecular surfaces.
• To enable direct use of generated meshes in subsequent surface-conforming volume mesh generation for FEM simulations.

Main Methods:

• The method is based on a trace technique, building upon previous work.
• It divides the Gaussian surface into single-valued pieces along x, y, and z directions.
• This division is achieved by tracing extreme points along fold curves on the surface.

Main Results:

• The developed method successfully generates surface meshes that are manifold.
• The meshes produced preserve the original topology of the molecular Gaussian surface.
• Numerical tests confirm the avoidance of intersections and the generation of closed, valid surface meshes.

Conclusions:

• The improved meshing method effectively addresses common defects in molecular surface mesh generation.
• The resulting manifold meshes are suitable for direct use in BEM and FEM simulations.
• This advancement facilitates more robust and efficient mathematical simulations of biomolecules.