IMR08 - Alper ngr University of Florida Mathematical...

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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 non-incident 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 non-acute angles undesired elements stretched in certain directions are desired Quality Constraint Quality Constraint Smallest Angle Aspect ratio circumradius inradius Radius-edge 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 radius-edge 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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IMR08 - Alper ngr University of Florida Mathematical...

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