Cleaver A new tetrahedral mesher Landscape Bio Mesh

Cleaver A new tetrahedral mesher.

Landscape • Bio. Mesh 3 D o o o State of the start Adaptive Mostly good quality elements May produce degenerate elements Variational / Computational Expensive Unstructured Meshes • Cleaver o o o No degenerate elements. Bounded worst-case element quality Guarantees on conformity / fidelity Structured Fast

Element Quality • Dihedral Angles • Condition Number 1. 00 E+20 1. 00 E+18 Condition Number 1. 00 E+16 1. 00 E+14 1. 00 E+12 1. 00 E+10 1. 00 E+08 1. 00 E+06 6. 4551 1. 9865 0. 2215 0. 0806 Worst Dihedral Angle 0. 0306 0. 008

Multi-Material Challenges • Higher dimensional features • Interfaces may form sharp cusps • Complexity of cases o Arbitrarily many cases even with linear elements o Not all representable o Snaps/warps more constrained

Cleaver • Based on Lattice Cleaving algorithm o "Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality” o Bronson, J. , Levine, J. , and Whitaker, R. o To appear in Proceedings of the 21 st International Meshing Roundtable (San Jose, CA, Oct 7 - 10, 2012) • Combinatoric (not variational) o Background mesh (structured) o Stencils to capture surfaces • Inherent Tradeoff o Deforming background grid (small deviations) o Cutting / Subdividing (large deviations)

Stencils • Background lattice composed of tetrahedra which are ‘cleaved’ into various stencils. • These stencils locally capture various topologies

Graded Background Octree Structure Background Stencils

Dihedral Angles Min: 2. 76 Max: 175. 42

Cleaver

Evaluation (Qual. ) Bio. Mesh 3 D Cleaver

Other Domains

Cleaver • First Release: • Features Fall 2012 Incredibly fast Conforming Guarantees on Quality Input support • SCIRun NRRD format o Output supports • SCIRun pts/elems • Tetgen node/eles • MATLAB Binaries o o