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.

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.

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.

A New Global Optimization Algorithm and its Application

2008 ◽  
Vol 33-37 ◽  
pp. 1407-1412
Author(s):  
Ying Hui Lu ◽  
Shui Lin Wang ◽  
Hao Jiang ◽  
Xiu Run Ge
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Inverse Analysis ◽  
Optimization Problem ◽  
Practical Application ◽  
Global Optimization Algorithm ◽  
Material Parameters ◽  
Non Linear ◽  
Variable Space

In geotechnical engineering, based on the theory of inverse analysis of displacement, the problem for identification of material parameters can be transformed into an optimization problem. Commonly, because of the non-linear relationship between the identified parameters and the displacement, the objective function bears the multimodal characteristic in the variable space. So to solve better the multimodal characteristic in the non-linear inverse analysis, a new global optimization algorithm, which integrates the dynamic descent algorithm and the modified BFGS (Brogden-Fletcher-Goldfrab-Shanno) algorithm, is proposed. Five typical multimodal functions in the variable space are tested to prove that the new proposed algorithm can quickly converge to the best point with few function evaluations. In the practical application, the new algorithm is employed to identify the Young’s modulus of four different materials. The results of the identification further show that the new proposed algorithm is a very highly efficient and robust one.

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