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

CS 101 - Meshing Winter 2007

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Adaptive Mesh Refinement

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Mesh Refinement

Applications

reduce error in simulations approximation

quality

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Delaunay Refinement

Ruppert/Chew

quality measure: circumradius to

shortest edge

angle lower bound

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Delaunay Refinement

Split triangles

insert circumcenter of low quality

triangles

new edges termination assured:

no new edge shorter vertices can’t be too close…

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Insertion

Incremental insertion

point location recover Delaunay

Boyer/Watson Edge flip

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Boundaries…

Circumcenter could be outside

split all segments

any circumcircle

has center inside

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Ruppert

Want mesh grading

bisect encroached segments

vertex in min-containment ball

Delaunay refine

BUT, avoid

encroachment

bisect segment instead

termination for

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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…

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Other Methods

Longest edge bisection

Rivara many flavors…

Hierarchies

binary splits/quad splits adaptive trees restriction criteria (hanging nodes)