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.

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.

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 Composite Differential Search Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Bo Liu
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Control Parameters ◽  
Original Algorithm ◽  
New Space ◽  
Random Method ◽  
Better Than

Differential search algorithm (DS) is a relatively new evolutionary algorithm inspired by the Brownian-like random-walk movement which is used by an organism to migrate. It has been verified to be more effective than ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES. In this paper, we propose four improved solution search algorithms, namely “DS/rand/1,” “DS/rand/2,” “DS/current to rand/1,” and “DS/current to rand/2” to search the new space and enhance the convergence rate for the global optimization problem. In order to verify the performance of different solution search methods, 23 benchmark functions are employed. Experimental results indicate that the proposed algorithm performs better than, or at least comparable to, the original algorithm when considering the quality of the solution obtained. However, these schemes cannot still achieve the best solution for all functions. In order to further enhance the convergence rate and the diversity of the algorithm, a composite differential search algorithm (CDS) is proposed in this paper. This new algorithm combines three new proposed search schemes including “DS/rand/1,” “DS/rand/2,” and “DS/current to rand/1” with three control parameters using a random method to generate the offspring. Experiment results show that CDS has a faster convergence rate and better search ability based on the 23 benchmark functions.

A log-barrier method for mesh quality improvement and untangling

2012 ◽  
Vol 30 (3) ◽  
pp. 315-329 ◽  
Author(s):  
Shankar P. Sastry ◽  
Suzanne M. Shontz ◽  
Stephen A. Vavasis
Keyword(s):  
Quality Improvement ◽  
Mesh Quality ◽  
Barrier Method ◽  
Mesh Quality Improvement
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