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in subjects: "Jacobian Function"

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Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number

We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the te… more

Date: September 27, 1999

Creator: Freitag, Lori A. & Knupp, Patrick

Item Type: Article

Partner: UNT Libraries Government Documents Department

open access

Matrix Norms and the Condition Number: A General Framework to Improve Mesh Quality via Node-Movement

Objective functions for unstructured hexahedral and tetrahedral mesh optimization are analyzed using matrices and matrix norms. Mesh untangling objective functions that create valid meshes are used to initialize the optimization process. Several new objective functions to achieve element invertibility and quality are investigated, the most promising being the ''condition number''. The condition number of the Jacobian matrix of an element forms the basis of a barrier-based objective function tha… more

Date: September 27, 1999

Creator: Knupp, Patrick