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

Kim, Jibum; Shin, Myeonggyu; Kang, Won‐Hee

doi:10.1155/2015/264741

Cited by 5 publications

(16 citation statements)

References 21 publications

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“…Since the objective function defined in Equation (2) is a non-smooth objective function, we use a downhill simplex method to minimize it. The downhill simplex method is a popular derivative-free method, which does not use either function derivatives or a Hessian, but only uses function evaluations [15]. It first generates a virtual initial simplex to begin, which is a triangle in 2D and removes the vertex with the worst function value and replace it with another point with a better value by repeatedly performing three actions to find the optimal point: expansions, reflections, and contractions [16].…”

Section: Mesh Quality Improvementmentioning

confidence: 99%

“…It first generates a virtual initial simplex to begin, which is a triangle in 2D and removes the vertex with the worst function value and replace it with another point with a better value by repeatedly performing three actions to find the optimal point: expansions, reflections, and contractions [16]. Readers refer to [15,16] for more details on the downhill simplex method.…”

Section: Mesh Quality Improvementmentioning

confidence: 99%

“…When the downhill simplex method is used, initial simplex diameter should be appropriately chosen such that the mesh optimization process converges quickly. Based on the observation in [15], we choose an initial simplex diameter to be 0.1× (minimum edge length).…”

Section: Mesh Quality Improvementmentioning

confidence: 99%

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

Choi

Kim²,

Sastry³

et al. 2019

Symmetry

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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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Section: Mesh Quality Improvementmentioning

confidence: 99%

Section: Mesh Quality Improvementmentioning

confidence: 99%

See 1 more Smart Citation

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

Choi

Kim²,

Sastry³

et al. 2019

Symmetry

Self Cite

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show abstract

“…It uses the mesh quality metric to evaluate element quality and formulates a numerical optimization problem that guides vertex movement to improve the quality [11]. Various nonlinear solvers, such as nonlinear steepest descent and conjugate gradient methods, have been developed to solving the numerical optimization problem [10], [12].…”

Section: Introductionmentioning

confidence: 99%

A Data-Driven Approach for Simultaneous Mesh Untangling and Smoothing Using Pointer Networks

2020

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Poorly-shaped and/or inverted elements negatively affect numerical simulation accuracy and efficiency. Most current approaches consider mesh quality improvement and mesh untangling problems as numerical optimization problems and solve them using nonlinear optimization. However, these optimization-based approaches require users to set and solve complex numerical optimization problems with no guarantee that the output meshes are valid meshes with good element qualities. Therefore, this paper proposes a data-driven approach for simultaneous mesh untangling and smoothing using a Pointer network. The proposed approach generates various triangular meshes and employs a novel sequence generation algorithm to train the Pointer network and predicts competitive approximate solutions using the trained network. The strength of the proposed framework lies in its simplicity to predict the best free vertex candidate, providing high-quality output meshes, since it does not require solving complex numerical optimization for prediction. Experimental results show that the proposed framework successfully eliminates inverted elements on the meshes and improved average and worst element quality up to 85.9% and 97.8%, respectively, compared to current optimization-based methods. INDEX TERMS Mesh smoothing, mesh untangling, pointer network, deep learning, recurrent neural network.

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“…The idea is untangle the mesh and, at the same time, improve the quality of all elements. Typical quality measures involve the condition number and determinant of the Jacobian matrix [10,12], mean-ratio [9,13], among others [11,14,15]. This procedure defines an optimization problem:…”

mentioning

confidence: 99%

Compressible Flow Simulations with an Spectral Difference Method and Using High-Order Boundary Treatment

Martini¹,

Aguiar²,

Azevedo³

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. The present work addresses several aspects associated with an efficient use of the high-order Spectral Difference (SD) method for the simulation of compressible flows. Flows of interest are assumed to be adequately modeled by the two-dimensional (2-D) Euler or the 2-D Navier-Stokes equations. Issues associated with the use of curved boundaries are discussed. Namely, for special cases where highly stretched meshes are required, the problem of auto-intersecting elements is highlighted. Further developments on general order meshes with an attention to node positioning are also discussed. Motivated primarily by the needs of compressible viscous flows, the use of radial basis functions and mesh optimization will be discussed in order to accommodate the interior nodes. Furthermore, an important validation test for curved meshes is addressed, in order to demonstrate the capability implemented.

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

Cited by 5 publications

References 21 publications

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

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

A Data-Driven Approach for Simultaneous Mesh Untangling and Smoothing Using Pointer Networks

Compressible Flow Simulations with an Spectral Difference Method and Using High-Order Boundary Treatment

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