Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
In this research, a procedure called the Reference Jacobian based Mesh Optimization has been developed for the optimization of 3D mesh quality by node repositioning. The procedure is designed to improve the quality or geometric shape of mesh regions and boundary mesh faces while keeping the improved mesh as close as possible to the original mesh. The quality measure optimized in the procedure is the Condition Number shape measure which quantifies the distortion of a trivalent element corner from an "ideal" corner of a canonical element. This "ideal" corner is usually considered to be formed by 3 unit vectors coincident at the origin and lying along the coordinate axes but any other definition may be used in its place.
The procedure also includes a method for improving the quality of mesh faces on internal and external boundaries while preserving surface characteristics as described in the articles on polygonal surface mesh quality improvement.
The overall procedure consists of iterations involving node repositioning on the boundary followed by node repositioning in the interior (with boundary nodes fixed).
The procedure has proved to be very effective in improving mesh quality of multi-material tetrahedral and hexahedral meshes while minimizing changes to the mesh characteristics and to the discrete boundary surfaces.
Figures below show a cut-away view of the volume mesh of a pig before and after optimization using two different quality optimization procedures. The top center picture shows the initial mesh, the bottom left picture shows an optimized mesh where the quality of the mesh is improved while keeping the nodes close to their original positions and the bottom right picture shows an optimized mesh where the quality of the mesh is improved as much as possible.
