Adaptive Skin Meshes Coarsening for Biomolecular Simulation

Area of Science:

• Computational chemistry
• Computer graphics
• Scientific computing

Background:

• Generating accurate and efficient volumetric meshes for molecular surfaces is crucial for computational simulations.
• Existing methods may struggle with guaranteed quality, adaptive refinement, or compatibility with multigrid solvers.

Purpose of the Study:

• To present efficient algorithms for generating hierarchical molecular skin meshes.
• To ensure guaranteed quality for both surface and volumetric meshes.
• To facilitate fast and accurate multigrid partial differential equation (PDE) solvers.

Main Methods:

• Algorithms generate a sequence of progressively coarser surface and volumetric meshes.
• Surface meshes adapt to curvature, maintaining topology and quality.
• Tetrahedral meshes conform to surface meshes, ensuring high-quality tetrahedra for interior and surrounding regions.
• Delaunay meshing ensures quality and geometric adaptivity.

Main Results:

• Hierarchical molecular skin meshes with decreasing size and guaranteed quality are generated.
• Surface meshes are adaptive to curvature and maintain topology.
• Conforming tetrahedral meshes decompose molecular interiors and surrounding regions.
• Meshes are Delaunay and geometrically adaptive.

Conclusions:

• The developed hierarchical tetrahedral meshes offer significant advantages for multigrid PDE solvers.
• Guaranteed mesh quality, accurate boundary approximation, and geometric adaptivity are key benefits.
• These meshes provide a robust foundation for advanced molecular simulations.