scholarly journals Two derivative-free optimization algorithms for mesh quality improvement

2010 ◽  
Vol 1 (1) ◽  
pp. 387-396 ◽  
Author(s):  
Jeonghyung Park ◽  
Suzanne M. Shontz
Keyword(s):  
Quality Improvement ◽  
Optimization Algorithms ◽  
Mesh Quality ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Mesh Quality Improvement

scholarly journals A Derivative-Free Mesh Optimization Algorithm for Mesh Quality Improvement and Untangling

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jibum Kim ◽  
Myeonggyu Shin ◽  
Woochul Kang
Keyword(s):  
Quality Improvement ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problem ◽  
Numerical Results ◽  
Mesh Optimization ◽  
Mesh Quality ◽  
Derivative Free ◽  
Downhill Simplex ◽  
Mesh Quality Improvement

We propose a derivative-free mesh optimization algorithm, which focuses on improving the worst element quality on the mesh. The mesh optimization problem is formulated as a min-max problem and solved by using a downhill simplex (amoeba) method, which computes only a function value without needing a derivative of Hessian of the objective function. Numerical results show that the proposed mesh optimization algorithm outperforms the existing mesh optimization algorithm in terms of improving the worst element quality and eliminating inverted elements on the mesh.

Tuning BARON using derivative-free optimization algorithms

2018 ◽  
Vol 74 (4) ◽  
pp. 611-637 ◽  
Author(s):  
Jianfeng Liu ◽  
Nikolaos Ploskas ◽  
Nikolaos V. Sahinidis
Keyword(s):  
Optimization Algorithms ◽  
Derivative Free Optimization ◽  
Derivative Free

A Framework for Finite Element Mesh Quality Improvement and Visualization in Orthopaedic Biomechanics

2009 ◽  
Author(s):  
Kiran H. Shivanna ◽  
Srinivas C. Tadepalli ◽  
Vincent A. Magnotta ◽  
Nicole M. Grosland
Keyword(s):  
Finite Element ◽  
Quality Improvement ◽  
Biological Processes ◽  
Mesh Quality ◽  
The Finite Element Method ◽  
Element Mesh ◽  
Invaluable Tool ◽  
Finite Element Meshing ◽  
Mesh Quality Improvement

The finite element method (FEM) is an invaluable tool in the numerical simulation of biological processes. FEM entails discretization of the structure of interest into elements. This discretization process is termed finite element meshing. The validity of the solution obtained is highly dependent on the quality of the mesh used. Mesh quality can decrease with increased complexity of the structure of interest, as is often evident when meshing biologic structures. This necessitated the development/implementation of generalized mesh quality improvement algorithms.

scholarly journals Benchmarking Derivative-Free Optimization Algorithms

2009 ◽  
Vol 20 (1) ◽  
pp. 172-191 ◽  
Author(s):  
Jorge J. Moré ◽  
Stefan M. Wild
Keyword(s):  
Optimization Algorithms ◽  
Derivative Free Optimization ◽  
Derivative Free

scholarly journals A Deviation-Based Dynamic Vertex Reordering Technique for 2D Mesh Quality Improvement

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 895 ◽  
Author(s):  
Junhyeok Choi ◽  
Harrim Kim ◽  
Shankar Prasad Sastry ◽  
Jibum Kim
Keyword(s):  
Quality Improvement ◽  
Optimization Problem ◽  
Mesh Optimization ◽  
Mesh Quality ◽  
Free Vertex ◽  
Smooth Optimization ◽  
Downhill Simplex ◽  
Mesh Quality Improvement ◽  
Better Than

We propose a novel deviation-based vertex reordering method for 2D mesh quality improvement. We reorder free vertices based on how likely this is to improve the quality of adjacent elements, based on the gradient of the element quality with respect to the vertex location. Specifically, we prioritize the free vertex with large differences between the best and the worst-quality element around the free vertex. Our method performs better than existing vertex reordering methods since it is based on the theory of non-smooth optimization. The downhill simplex method is employed to solve the mesh optimization problem for improving the worst element quality. Numerical results show that the proposed vertex reordering techniques improve both the worst and average element, compared to those with existing vertex reordering techniques.

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