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Global Optimization of Mesh Quality



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Global Optimization of Mesh Quality David Eppstein Univ of California Irvine Dept of Information and Computer Science Global optimization of mesh quality 1 D Eppstein Meshing Roundtable 2001 Outline Introduction Mesh quality issues meshing steps Connectivity optimization Delaunay triangulation edge insertion Global point placement Quadtrees incremental Delaunay refinement Individual point placement Quasiconvex programming sliver exudation Global optimization of mesh quality 2 D Eppstein Meshing Roundtable 2001 I What is Meshing Given an input domain manifold with boundary or possibly non manifold geometry Partition it into simple cells triangles quadrilaterals tetrahedra cuboids Essential preprocessing step for finite element method numerical solution of differential equations e g airflow Other applications e g computer graphics Global optimization of mesh quality 3 D Eppstein Meshing Roundtable 2001 Triangle mesh of Lake Superior Ruppert Global optimization of mesh quality 4 D Eppstein Meshing Roundtable 2001 Quadrilateral mesh of an irregular polygon all quadrilaterals kite shaped Global optimization of mesh quality 5 D Eppstein Meshing Roundtable 2001 Triangle mesh on three dimensional surface Chew Global optimization of mesh quality 6 D Eppstein Meshing Roundtable 2001 Tetrahedral mesh of a cube Global optimization of mesh quality 7 D Eppstein Meshing Roundtable 2001 Portion of hexahedral mesh of elbow pipe Tautges and Mitchell Global optimization of mesh quality 8 D Eppstein Meshing Roundtable 2001 Mesh Quality Issues Element type 2d triangles vs quadrilaterals 3d tetrahedra vs hexahedra This talk primarily triangles and tetrahedra Quality guarantees for quad hex meshes much less developed Element shape Avoid sharp angles flat angles distorted elements Affects accuracy of numerical simulation Element size Need small elements near small features or abrupt changes in solution large elements ok in uninteresting parts of domain Number of elements More elements



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