Local optimization-based simplicial mesh untangling and improvement.

Journal Article · Sun Sep 10 04:00:00 EDT 2000 · Int. J. Numer. Methods Eng.

DOI:https://doi.org/10.1002/1097-0207(20000910/20)49:1/2<109::AID-NME925>3.3.CO;2-L· OSTI ID:942567

Freitag, L A; Plassmann, P

We present an optimization-based approach for mesh untangling that maximizes the minimum area or volume of simplicial elements in a local submesh. These functions are linear with respect to the free vertex position; thus the problem can be formulated as a linear program that is solved by using the computationally inexpensive simplex method. We prove that the function level sets are convex regardless of the position of the free vertex, and hence the local subproblem is guaranteed to converge. Maximizing the minimum area or volume of mesh elements, although well suited for mesh untangling, is not ideal for mesh improvement, and its use often results in poor quality meshes. We therefore combine the mesh untangling technique with optimization-based mesh improvement techniques and expand previous results to show that a commonly used two-dimensional mesh quality criterion can be guaranteed to converge when starting with a valid mesh. Typical results showing the effectiveness of the combined untangling and smoothing techniques are given for both two- and three- dimensional simplicial meshes.

• Research Organization: Argonne National Laboratory (ANL)
• Sponsoring Organization: SC
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 942567
• Report Number(s): ANL/MCS/JA-32634
• Journal Information: Int. J. Numer. Methods Eng., Journal Name: Int. J. Numer. Methods Eng. Journal Issue: 1-2 ; Sep. 10, 2000 Vol. 49; ISSN IJNMBH; ISSN 0029-5981
• Country of Publication: United States
• Language: ENGLISH

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CALCULATION METHODS
COMPUTER CALCULATIONS
LINEAR PROGRAMMING
MESH GENERATION
OPTIMIZATION
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS