NDLI: A log-barrier method for mesh quality improvement and untangling

Content Provider	Springer Nature Link
Author	Sastry, Shankar P. Shontz, Suzanne M. Vavasis, Stephen A.
Copyright Year	2012
Abstract	The presence of a few inverted or poor-quality mesh elements can negatively affect the stability, convergence and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement and untangling method that untangles a mesh with inverted elements and improves its quality. Worst element mesh quality improvement and untangling can be formulated as a nonsmooth unconstrained optimization problem, which can be reformulated as a smooth constrained optimization problem. Our technique solves the latter problem using a log-barrier interior point method and uses the gradient of the objective function to efficiently converge to a stationary point. The method uses a logarithmic barrier function and performs global mesh quality improvement. We have also developed a smooth quality metric that takes both signed area and the shape of an element into account. This quality metric assigns a negative value to an inverted element. It is used with our algorithm to untangle a mesh by improving the quality of an inverted element to a positive value. Our method usually yields better quality meshes than existing methods for improvement of the worst quality elements, such as the active set, pattern search, and multidirectional search mesh quality improvement methods. Our method is faster and more robust than existing methods for mesh untangling, such as the iterative stiffening method.
Starting Page	315
Ending Page	329
Page Count	15
File Format	PDF
ISSN	01770667
Journal	Engineering with Computers
Volume Number	30
Issue Number	3
e-ISSN	14355663
Language	English
Publisher	Springer London
Publisher Date	2012-11-24
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mesh quality improvement Mesh optimization Mesh untangling Interior point method Log-barrier Computer-Aided Engineering (CAD, CAE) and Design Math. Applications in Chemistry Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Mechanics ApplicationMathematics/Computational Methods of Engineering
Content Type	Text
Resource Type	Article
Subject	Engineering Computer Science Applications Modeling and Simulation Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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