1. Converting a Tetrahedral Mesh to a Prism-Tetrahedral Hybrid Mesh for FEM Accuracy and Efficiency
Soji Yamakawa and Kenji Shimada
GOAL
Converting a tetrahedral mesh into a prism-tetrahedral mixed mesh. A prism-tetrahedral hybrid mesh yields a more accurate FEM solution with less computational time than a tetrahedral mesh.
APPROACH
The proposed method progressively inserts layers of prism elements in sweepable sub-volumes starting from a given cross section.
Prism-Layer Insertion
Input Tetrahedral Mesh 5,994 nodes 25,013 elements
After 4 Layers are Inserted
Final Prism+Tet Mesh 5,858 nodes 18,319 tet elements 1,960 prism elements 20,279 elements in total
No more prism layer can be inserted without violating a prescribed quality threshold
Frontal Plane
Cutting Plane (Initial Frontal Plane)
Cross Section
Undo-able Data Structure
Apply sequence of edge-collapse, local transformation, and smoothing operations to remove nodes that obstructs a new prism layer
A new prism layer is inserted if:
(1) All nodes obstructing the new layer insertion are removed, and (2) No element violates the quality threshold.
Undo-able data structure overcomes the order-dependency problem of the mesh-modifying operations.
If an element violates the quality threshold, the modifications must be retracted, and the proposed method tries a different sequence of mesh-modifying operations
Effect of the Prism-Layer Insertion
Error
Tetrahedral Mesh
Prism-Tet Hybrid Mesh
20000
40000
60000
80000
100000
# of elements
Convergence of the Error Between Two Outlet Fluxes
CFD Analysis of an Air-Conditioner Duct
CFD Solution converges (reaches as accurate as it can) faster with a prism-tet hybrid mesh than a tetrahedral mesh.
Structural Analysis of a Leg-Bone