Adaptive skin meshes coarsening for biomolecular simulation

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedra that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry.

► We present efficient algorithm for generating hierarchical meshes with high quality.
► Our algorithm generate coarse meshes for both the surfaces and their volumes.
► Surface mesh is adaptive to the surface curvature with guaranteed mesh quality.
► Tetrahedral mesh conforms to the interface surface mesh with quality guarantee.
► These meshes are desirable in computational biology for biomolecular simulation.