Algebraic mesh quality metrics for unstructured initial meshes
Finite Elements in Analysis and Design
Analysis of triangle quality measures
Mathematics of Computation
A geometric diagram and hybrid scheme for triangle subdivision
Computer Aided Geometric Design
Streaming tetrahedral mesh optimization
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Streaming Mesh Optimization for CAD
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Computer Methods and Programs in Biomedicine
The challenge of hexahedral meshing of arterial geometry
Machine Graphics & Vision International Journal
An automatic strategy for adaptive tetrahedral mesh generation
Applied Numerical Mathematics
Technical Section: Quality encoding for tetrahedral mesh optimization
Computers and Graphics
Adaptive mesh coarsening for quadrilateral and hexahedral meshes
Finite Elements in Analysis and Design
Smoothing and local refinement techniques for improving tetrahedral mesh quality
Computers and Structures
Shape optimization of peristaltic pumping
Journal of Computational Physics
Improved objective functions for tetrahedral mesh optimisation
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Journal of Computational Physics
Journal of Computational Physics
Feature-based multiblock finite element mesh generation
Computer-Aided Design
A priori mesh quality metric error analysis applied to a high-order finite element method
Journal of Computational Physics
Quality tetrahedral mesh smoothing via boundary-optimized Delaunay triangulation
Computer Aided Geometric Design
Finite Elements in Analysis and Design
SMI 2013: Efficient computation of constrained parameterizations on parallel platforms
Computers and Graphics
Journal of Biomedical Imaging
A surface mesh smoothing and untangling method independent of the CAD parameterization
Computational Mechanics
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Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. The singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. The condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Two combined metrics, shape-volume and shape-volume orientation, are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to nonsimplicial elements. A series of numerical tests verifies the theoretical properties of the metrics defined.