Adaptive Mesh Refinement CS 101 - Meshing Winter 2007 1 Mesh - PDF document

Adaptive Mesh Refinement CS 101 - Meshing Winter 2007 1 Mesh Refinement Applications � reduce error in simulations � approximation quality CS 101 - Meshing Winter 2007 2

Delaunay Refinement Ruppert/Chew � quality measure: circumradius to shortest edge � angle lower bound CS 101 - Meshing Winter 2007 3 Delaunay Refinement Split triangles � insert circumcenter of low quality triangles � new edges � termination assured: � no new edge shorter � vertices can’t be too close… CS 101 - Meshing Winter 2007 4

Insertion Incremental insertion � point location � recover Delaunay Edge flip Boyer/Watson CS 101 - Meshing Winter 2007 5 Boundaries… Circumcenter could be outside � split all segments � any circumcircle has center inside CS 101 - Meshing Winter 2007 6

Ruppert Want mesh grading � bisect encroached segments � vertex in min-containment ball � Delaunay refine � BUT, avoid encroachment � bisect segment instead � termination for CS 101 - Meshing Winter 2007 7 Ruppert in 3D Shewchuk � avoid encroachment � first 1D, then 2D � Delaunay insert circumcenters � UNLESS: encroachment would result � in that case: split lower D instead � tons of details… CS 101 - Meshing Winter 2007 8

Other Methods Longest edge bisection � Rivara � many flavors… Hierarchies � binary splits/quad splits � adaptive trees � restriction criteria (hanging nodes) CS 101 - Meshing Winter 2007 9