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Unformatted text preview: Alper ngr University of Florida Mathematical Foundations of Mesh Generation *OUFSOBUJPOBM .FTIJOH 3PVOEUBCMF 1JUUTICVSHI Compute quickly the smallest size ( simplicial, cubical) mesh of a given domain such that all the elements are of good quality . Meshing Problem Applications: Engineering, Graphics, Visualization, GIS, CAD, Medical Imaging, Computational Biology... Compute quickly the smallest size ( simplicial, cubical) mesh of a given domain such that all the elements are of good quality . Meshing Problem Applications: Engineering, Graphics, Visualization, GIS, CAD, Medical Imaging, Computational Biology... Compute quickly the smallest size ( simplicial, cubical) mesh of a given domain such that all the elements are of good quality . Meshing Problem Applications: Engineering, Graphics, Visualization, GIS, CAD, Medical Imaging, Computational Biology... Compute quickly the smallest size ( simplicial, cubical) mesh of a given domain such that all the elements are of good quality . Meshing Problem Applications: Engineering, Graphics, Visualization, GIS, CAD, Medical Imaging, Computational Biology... Compute quickly the smallest size ( simplicial, cubical) mesh of a given domain such that all the elements are of good quality . Meshing Problem Applications: Engineering, Graphics, Visualization, GIS, CAD, Medical Imaging, Computational Biology... Input: PSLG A collection of vertices and segments is called a planar straight line graph (PSLG) if both endpoints of any segment in are vertices of ; two segments in intersect only at their endpoints. Local Feature Size Definition. The local feature size at point x of a domain , lfs ( x ) , is the radius of the smallest ball at x that intersects two nonincident features of . lfs( p ) lfs( q ) +  pq  (Lipschitz property) INPUT: PLC A collection of vertices, segments, and facet is called a pievewise linear complex (PLC) [MillerTTW96] if boundary of an element in also belong to ; two elements intersect only at the elements of . Bad quality elements cause interpolation, conditioning, discretization errors BabuskaA76, Knupp98, Shewchuk02 Various quality criteria: small angles undesired large angles undesired obtuse or nonacute angles undesired elements stretched in certain directions are desired Quality Constraint Quality Constraint Smallest Angle Aspect ratio circumradius inradius Radiusedge ratio circumradius shortest edge a ! /2 ! /2 c b R x x r z z y y R/r = (1 / ) ! ! ! a c b R R/  cb  = 1 / (2 sin ) QuaLITY in 3d a b c d radiusedge ratio vs. dihedral angles in 3D Size of the Mesh (# of elements) leads to faster numerical solution Size of the Elements geometric vs. numeric constraint SIZE Constraint Size of the Mesh (# of elements) leads to faster numerical solution Size of the Elements geometric vs. numeric constraint SIZE Constraint Advancing Front Heuristics...
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 Fall '08
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