Journal articles: 'Gradient Smoothing'

1

Fang, Shuai, Zhenji Yao, and Jing Zhang. "Scale and Gradient Aware Image Smoothing." IEEE Access 7 (2019): 166268–81. http://dx.doi.org/10.1109/access.2019.2953550.

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Wang, Dongdong, Jiarui Wang, and Junchao Wu. "Superconvergent gradient smoothing meshfree collocation method." Computer Methods in Applied Mechanics and Engineering 340 (October 2018): 728–66. http://dx.doi.org/10.1016/j.cma.2018.06.021.

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Zhou, Zhengyong, and Qi Yang. "An Active Set Smoothing Method for Solving Unconstrained Minimax Problems." Mathematical Problems in Engineering 2020 (June 24, 2020): 1–25. http://dx.doi.org/10.1155/2020/9108150.

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In this paper, an active set smoothing function based on the plus function is constructed for the maximum function. The active set strategy used in the smoothing function reduces the number of gradients and Hessians evaluations of the component functions in the optimization. Combing the active set smoothing function, a simple adjustment rule for the smoothing parameters, and an unconstrained minimization method, an active set smoothing method is proposed for solving unconstrained minimax problems. The active set smoothing function is continuously differentiable, and its gradient is locally Lipschitz continuous and strongly semismooth. Under the boundedness assumption on the level set of the objective function, the convergence of the proposed method is established. Numerical experiments show that the proposed method is feasible and efficient, particularly for the minimax problems with very many component functions.

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Xu, Li, Cewu Lu, Yi Xu, and Jiaya Jia. "Image smoothing via L 0 gradient minimization." ACM Transactions on Graphics 30, no. 6 (December 2011): 1–12. http://dx.doi.org/10.1145/2070781.2024208.

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Burke, James V., Tim Hoheisel, and Christian Kanzow. "Gradient Consistency for Integral-convolution Smoothing Functions." Set-Valued and Variational Analysis 21, no. 2 (March 29, 2013): 359–76. http://dx.doi.org/10.1007/s11228-013-0235-6.

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Pinilla, Samuel, Tamir Bendory, Yonina C. Eldar, and Henry Arguello. "Frequency-Resolved Optical Gating Recovery via Smoothing Gradient." IEEE Transactions on Signal Processing 67, no. 23 (December 1, 2019): 6121–32. http://dx.doi.org/10.1109/tsp.2019.2951192.

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Avrashi, Jacob. "High order gradient smoothing towards improved C1 eigenvalues." Engineering Computations 12, no. 6 (June 1995): 513–28. http://dx.doi.org/10.1108/02644409510799749.

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Wang, Bao, Difan Zou, Quanquan Gu, and Stanley J. Osher. "Laplacian Smoothing Stochastic Gradient Markov Chain Monte Carlo." SIAM Journal on Scientific Computing 43, no. 1 (January 2021): A26—A53. http://dx.doi.org/10.1137/19m1294356.

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Lin, Qihang, Xi Chen, and Javier Peña. "A smoothing stochastic gradient method for composite optimization." Optimization Methods and Software 29, no. 6 (March 13, 2014): 1281–301. http://dx.doi.org/10.1080/10556788.2014.891592.

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He, Liangtian, and Yilun Wang. "Image smoothing via truncated ℓ 0 gradient regularisation." IET Image Processing 12, no. 2 (February 1, 2018): 226–34. http://dx.doi.org/10.1049/iet-ipr.2017.0533.

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Liu, Qian, Caiming Zhang, Qiang Guo, and Yuanfeng Zhou. "A nonlocal gradient concentration method for image smoothing." Computational Visual Media 1, no. 3 (August 14, 2015): 197–209. http://dx.doi.org/10.1007/s41095-015-0012-6.

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Yao, Jianyao, Weimin Wu, Kun Zhang, Dongyang Sun, Yaolu Liu, Huiming Ning, Ning Hu, and G. R. Liu. "Development of Three-Dimensional GSM-CFD Solver for Compressible Flows." International Journal of Computational Methods 14, no. 04 (April 18, 2017): 1750037. http://dx.doi.org/10.1142/s0219876217500372.

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A three-dimensional (3D) Computational Fluid Dynamics (CFD) solver based on the gradient smoothing method (GSM) is developed for compressible flows based on previous research. The piecewise constant smoothing function with one-point integration scheme is implemented for gradient approximation of field variables and convective fluxes. The matrix-based method for gradient approximations is also developed to improve the numerical efficiency. Numerical examples of gradient approximations of several given functions have shown that the proposed GSM is more accurate and robust to mesh distortion. A transonic ONERA M6 wing is used to demonstrate the effectiveness of the proposed GSM-CFD solver.

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CUI, X. Y., G. Y. LI, and G. R. LIU. "AN EXPLICIT SMOOTHED FINITE ELEMENT METHOD (SFEM) FOR ELASTIC DYNAMIC PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340002. http://dx.doi.org/10.1142/s0219876213400021.

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This paper presents an explicit smoothed finite element method (SFEM) for elastic dynamic problems. The central difference method for time integration will be used in presented formulations. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In present method, the problem domain is first divided into elements as in the finite element method (FEM), and the elements are further subdivided into several smoothing cells. Cell-wise strain smoothing operations are used to obtain the stresses, which are constants in each smoothing cells. Area integration over the smoothing cell becomes line integration along its edges, and no gradient of shape functions is involved in computing the field gradients nor in forming the internal force. No mapping or coordinate transformation is necessary so that the element can be used effectively for large deformation problems. Through several examples, the simplicity, efficiency and reliability of the smoothed finite element method are demonstrated.

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Liu, Wenli, Xiaoni Chi, Qili Yang, and Ranran Cui. "Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem." Mathematical Problems in Engineering 2021 (January 23, 2021): 1–11. http://dx.doi.org/10.1155/2021/6674520.

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In this paper, a weighted second-order cone (SOC) complementarity function and its smoothing function are presented. Then, we derive the computable formula for the Jacobian of the smoothing function and show its Jacobian consistency. Also, we estimate the distance between the subgradient of the weighted SOC complementarity function and the gradient of its smoothing function. These results will be critical to achieve the rapid convergence of smoothing methods for weighted SOC complementarity problems.

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Crisan, D., and M. Ottobre. "Pointwise gradient bounds for degenerate semigroups (of UFG type)." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2195 (November 2016): 20160442. http://dx.doi.org/10.1098/rspa.2016.0442.

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In this paper, we consider diffusion semigroups generated by second-order differential operators of degenerate type. The operators that we consider do not , in general, satisfy the Hörmander condition and are not hypoelliptic. In particular, instead of working under the Hörmander paradigm, we consider the so-called UFG (uniformly finitely generated) condition, introduced by Kusuoka and Strook in the 1980s. The UFG condition is weaker than the uniform Hörmander condition, the smoothing effect taking place only in certain directions (rather than in every direction, as it is the case when the Hörmander condition is assumed). Under the UFG condition, Kusuoka and Strook deduced sharp small time asymptotic bounds for the derivatives of the semigroup in the directions where smoothing occurs. In this paper, we study the large time asymptotics for the gradients of the diffusion semigroup in the same set of directions and under the same UFG condition. In particular, we identify conditions under which the derivatives of the diffusion semigroup in the smoothing directions decay exponentially in time. This paper constitutes, therefore, a stepping stone in the analysis of the long-time behaviour of diffusions which do not satisfy the Hörmander condition.

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Liu, G. R., and George X. Xu. "A gradient smoothing method (GSM) for fluid dynamics problems." International Journal for Numerical Methods in Fluids 58, no. 10 (December 10, 2008): 1101–33. http://dx.doi.org/10.1002/fld.1788.

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17

Xu, Mengwei, Soon-Yi Wu, and Jane J. Ye. "Solving semi-infinite programs by smoothing projected gradient method." Computational Optimization and Applications 59, no. 3 (March 19, 2014): 591–616. http://dx.doi.org/10.1007/s10589-014-9654-z.

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18

G R, Byra Reddy, and Prasanna Kumar H. "Smoothing of Mammogram Using an Improved Gradient based Technique." Advanced Biomedical Engineering 9 (2020): 202–8. http://dx.doi.org/10.14326/abe.9.202.

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19

Tian, Ying, and Haodi Ma. "L0 Gradient based Image Smoothing Method for Ear Identification." International Journal of Signal Processing, Image Processing and Pattern Recognition 8, no. 6 (June 30, 2015): 61–68. http://dx.doi.org/10.14257/ijsip.2015.8.6.08.

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20

Chen, Xi, Qihang Lin, Seyoung Kim, Jaime G. Carbonell, and Eric P. Xing. "Smoothing proximal gradient method for general structured sparse regression." Annals of Applied Statistics 6, no. 2 (June 2012): 719–52. http://dx.doi.org/10.1214/11-aoas514.

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21

Wu, Caiying, and Guoqing Chen. "A smoothing conjugate gradient algorithm for nonlinear complementarity problems." Journal of Systems Science and Systems Engineering 17, no. 4 (November 6, 2008): 460–72. http://dx.doi.org/10.1007/s11518-008-5091-9.

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22

Henderson, Daniel J., Qi Li, Christopher F. Parmeter, and Shuang Yao. "Gradient-based smoothing parameter selection for nonparametric regression estimation." Journal of Econometrics 184, no. 2 (February 2015): 233–41. http://dx.doi.org/10.1016/j.jeconom.2014.09.007.

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23

NGUYEN-THOI, T., P. PHUNG-VAN, T. RABCZUK, H. NGUYEN-XUAN, and C. LE-VAN. "AN APPLICATION OF THE ES-FEM IN SOLID DOMAIN FOR DYNAMIC ANALYSIS OF 2D FLUID–SOLID INTERACTION PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340003. http://dx.doi.org/10.1142/s0219876213400033.

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An edge-based smoothed finite element method (ES-FEM-T3) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the solid mechanics analyses. In this paper, the ES-FEM-T3 is further extended to the dynamic analysis of 2D fluid–solid interaction problems based on the pressure-displacement formulation. In the present coupled method, both solid and fluid domain is discretized by triangular elements. In the fluid domain, the standard FEM is used, while in the solid domain, we use the ES-FEM-T3 in which the gradient smoothing technique based on the smoothing domains associated with the edges of triangles is used to smooth the gradient of displacement. This gradient smoothing technique can provide proper softening effect, and thus improve significantly the solution of coupled system. Some numerical examples have been presented to illustrate the effectiveness of the proposed coupled method compared with some existing methods for 2D fluid–solid interaction problems.

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24

Mao, Zirui, and G. R. Liu. "A 3D Lagrangian gradient smoothing method framework with an adaptable gradient smoothing domain‐constructing algorithm for simulating large deformation free surface flows." International Journal for Numerical Methods in Engineering 121, no. 6 (November 11, 2019): 1268–96. http://dx.doi.org/10.1002/nme.6265.

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25

Chi, Xiaoni, Zhongping Wan, and Zijun Hao. "The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/965931.

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Second-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity functions, propose its smoothing function, and derive the computable formula for the Jacobian of the smoothing function. Based on these results, we prove the Jacobian consistency of the one-parametric class of smoothing functions, which will play an important role for achieving the rapid convergence of smoothing methods. Moreover, we estimate the distance between the subgradient of the one-parametric class of the SOC complementarity functions and the gradient of its smoothing function, which will help to adjust a parameter appropriately in smoothing methods.

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26

Chen, Miao, and Shou-qiang Du. "The Smoothing FR Conjugate Gradient Method for Solving a Kind of Nonsmooth Optimization Problem with l1-Norm." Mathematical Problems in Engineering 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/5817931.

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We study the method for solving a kind of nonsmooth optimization problems with l1-norm, which is widely used in the problem of compressed sensing, image processing, and some related optimization problems with wide application background in engineering technology. Transformated by the absolute value equations, this kind of nonsmooth optimization problem is rewritten as a general unconstrained optimization problem, and the transformed problem is solved by a smoothing FR conjugate gradient method. Finally, the numerical experiments show the effectiveness of the given smoothing FR conjugate gradient method.

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PRASATH, V. B. SURYA, and ARINDAMA SINGH. "AN ADAPTIVE DIFFUSION SCHEME FOR IMAGE RESTORATION AND SELECTIVE SMOOTHING." International Journal of Image and Graphics 12, no. 01 (January 2012): 1250003. http://dx.doi.org/10.1142/s0219467812500039.

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Anisotropic partial differential equation (PDE)-based image restoration schemes employ a local edge indicator function typically based on gradients. In this paper, an alternative pixel-wise adaptive diffusion scheme is proposed. It uses a spatial function giving better edge information to the diffusion process. It avoids the over-locality problem of gradient-based schemes and preserves discontinuities coherently. The scheme satisfies scale space axioms for a multiscale diffusion scheme; and it uses a well-posed regularized total variation (TV) scheme along with Perona-Malik type functions. Median-based weight function is used to handle the impulse noise case. Numerical results show promise of such an adaptive approach on real noisy images.

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28

De Silva, Kushani, Carlo Cafaro, and Adom Giffin. "Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework." Entropy 23, no. 6 (May 27, 2021): 674. http://dx.doi.org/10.3390/e23060674.

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Attaining reliable gradient profiles is of utmost relevance for many physical systems. In many situations, the estimation of the gradient is inaccurate due to noise. It is common practice to first estimate the underlying system and then compute the gradient profile by taking the subsequent analytic derivative of the estimated system. The underlying system is often estimated by fitting or smoothing the data using other techniques. Taking the subsequent analytic derivative of an estimated function can be ill-posed. This becomes worse as the noise in the system increases. As a result, the uncertainty generated in the gradient estimate increases. In this paper, a theoretical framework for a method to estimate the gradient profile of discrete noisy data is presented. The method was developed within a Bayesian framework. Comprehensive numerical experiments were conducted on synthetic data at different levels of noise. The accuracy of the proposed method was quantified. Our findings suggest that the proposed gradient profile estimation method outperforms the state-of-the-art methods.

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29

Yoon, Sangpil, Cheng-Tang Wu, Hui-Ping Wang, and Jiun-Shyan Chen. "Efficient Meshfree Formulation for Metal Forming Simulations." Journal of Engineering Materials and Technology 123, no. 4 (July 24, 2000): 462–67. http://dx.doi.org/10.1115/1.1396349.

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A stabilized conforming (SC) nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in collocation meshfree methods. The gradient matrix associated with strain smoothing satisfies the integration constraint (IC) of linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for history-dependent problems are introduced. Applications to metal forming analysis are presented, with the results demonstrating a significant improvement in computational efficiency without loss of accuracy.

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Pang, Xueshun, Suqi Zhang, Junhua Gu, Lingling Li, Boying Liu, and Huaibin Wang. "Improved L0 Gradient Minimization with L1 Fidelity for Image Smoothing." PLOS ONE 10, no. 9 (September 18, 2015): e0138682. http://dx.doi.org/10.1371/journal.pone.0138682.

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Li, Eric, Vincent Tan, George X. Xu, G. R. Liu, and Z. C. He. "A Novel Alpha Gradient Smoothing Method (αGSM) for Fluid Problems." Numerical Heat Transfer, Part B: Fundamentals 61, no. 3 (March 2012): 204–28. http://dx.doi.org/10.1080/10407790.2012.670562.

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YAO, JIANYAO, G. R. LIU, DONG QIAN, CHUNG-LUNG CHEN, and GEORGE X. XU. "A MOVING-MESH GRADIENT SMOOTHING METHOD FOR COMPRESSIBLE CFD PROBLEMS." Mathematical Models and Methods in Applied Sciences 23, no. 02 (January 8, 2013): 273–305. http://dx.doi.org/10.1142/s0218202513400046.

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A computational fluid dynamics (CFD) solver based on the gradient smoothing method (GSM) with moving mesh enabled is presented in this paper. The GSM uses unstructured meshes which could be generated and remeshed easily. The spatial derivatives of field variables at nodes and midpoints of cell edges are calculated using the gradient smoothing operations. The presented GSM codes use second-order Roes upwind flux difference splitting method and second-order 3-level backward differencing scheme for the compressible Navier–Stokes equations with moving mesh, and the second-order of accuracy for both the spatial and temporal discretization is ensured. The spatial discretization accuracy is verified using the method of manufactured solutions (MMS) on both structured and unstructured triangle meshes, and the results show that the observed order of accuracy achieves 2 even when highly distorted meshes are used. The temporal discretization accuracy is verified using the results with different time step lengths, and second-order accuracy is also obtained. Therefore, it is confirmed that the proposed GSM-CFD solver is a uniform second-order scheme.

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33

Ni, Kang, and Yiquan Wu. "Adaptive patched L0 gradient minimisation model applied on image smoothing." IET Image Processing 12, no. 10 (October 1, 2018): 1892–902. http://dx.doi.org/10.1049/iet-ipr.2017.1223.

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Kuprat, Andrew, Denise George, Eldon Linnebur, Harold Trease, and R. Kent Smith. "Moving Adaptive Unstructured 3-D Meshes in Semiconductor Process Modeling Applications." VLSI Design 6, no. 1-4 (January 1, 1998): 373–78. http://dx.doi.org/10.1155/1998/15828.

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The next generation of semiconductor process and device modeling codes will require 3-D mesh capabilities including moving volume and surface grids, adaptive mesh refinement and adaptive mesh smoothing. To illustrate the value of these techniques, a time dependent process simulation model was constructed using analytic functions to return time dependent dopant concentration and time dependent SiO2 volume and surface velocities. Adaptive mesh refinement and adaptive mesh smoothing techniques were used to resolve the moving boron dopant diffusion front in the Si substrate. The adaptive mesh smoothing technique involves minimizing the L2 norm of the gradient of the error between the true dopant concentration and the piecewise linear approximation over the tetrahedral mesh thus assuring that the mesh is optimal for representing evolving solution gradients. Also implemented is constrained boundary smoothing, wherein the moving SiO2/Si interface is represented by moving nodes that correctly track the interface motion, and which use their remaining degrees of freedom to minimize the aforementioned error norm. Thus, optimal tetrahedral shape and alignment is obtained even in the neighborhood of a moving boundary. If desired, a topological “reconnection” step maintains a Delaunay mesh at all times. The combination of adaptive refinement, adaptive smoothing, and mesh reconnection gives excellent front tracking, feature resolution, and grid quality for finite volume/finite element computation.

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Yang, Dakun, and Wei Wu. "A Smoothing Interval Neural Network." Discrete Dynamics in Nature and Society 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/456919.

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In many applications, it is natural to use interval data to describe various kinds of uncertainties. This paper is concerned with an interval neural network with a hidden layer. For the original interval neural network, it might cause oscillation in the learning procedure as indicated in our numerical experiments. In this paper, a smoothing interval neural network is proposed to prevent the weights oscillation during the learning procedure. Here, by smoothing we mean that, in a neighborhood of the origin, we replace the absolute values of the weights by a smooth function of the weights in the hidden layer and output layer. The convergence of a gradient algorithm for training the smoothing interval neural network is proved. Supporting numerical experiments are provided.

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36

Chipot, M., R. March, M. Rosati, and G. Vergara Caffarelli. "Analysis of a Nonconvex Problem Related to Signal Selective Smoothing." Mathematical Models and Methods in Applied Sciences 07, no. 03 (May 1997): 313–28. http://dx.doi.org/10.1142/s0218202597000189.

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We study some properties of a nonconvex variational problem. We fail to attain the infimum of the functional that has to be minimized. Instead, minimizing sequences develop gradient oscillations which allow them to reduce the value of the functional. We show an existence result for a perturbed nonconvex version of the problem, and we study the qualitative properties of the corresponding minimizer. The pattern of the gradient oscillations for the original nonperturbed problem is analyzed numerically.

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Li, Wei, Yingbin Chai, Xiangyu You, and Qifan Zhang. "An Edge-Based Smoothed Finite Element Method for Analyzing Stiffened Plates." International Journal of Computational Methods 16, no. 06 (May 27, 2019): 1840031. http://dx.doi.org/10.1142/s0219876218400315.

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In this paper, an edge-based smoothed finite element method with the discrete shear gap using triangular elements (ES-DSG3) is presented for static, free vibration and sound radiation analyses of plates stiffened by eccentric and concentric stiffeners. In the present model, the ES-DSG3 for the plate element with the isoparametric thick-beam element is employed to formulate stiffened plate structures. The deflections and rotations of the plates and the stiffeners are connected at tying positions. By using Rayleigh integral, sound radiation of stiffened plates subjected to a point load can be obtained. The edge-based gradient smoothing technique is employed to perform the related numerical integrations over the edge-based smoothing domains. Compared with the original DSG3 model, the present ES-DSG3 model is relatively softer as a result of the edge-based gradient smoothing technique. From several numerical examples, it is observed that the ES-DSG3 can produce more accurate numerical solutions than the original DSG3 for stiffened plates.

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LIU, G. R. "A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS." International Journal of Computational Methods 05, no. 02 (June 2008): 199–236. http://dx.doi.org/10.1142/s0219876208001510.

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This paper presents a generalized gradient smoothing technique, the corresponding smoothed bilinear forms, and the smoothed Galerkin weakform that is applicable to create a wide class of efficient numerical methods with special properties including the upper bound properties. A generalized gradient smoothing technique is first presented for computing the smoothed strain fields of displacement functions with discontinuous line segments, by "rudely" enforcing the Green's theorem over the smoothing domain containing these discontinuous segments. A smoothed bilinear form is then introduced for Galerkin formulation using the generalized gradient smoothing technique and smoothing domains constructed in various ways. The numerical methods developed based on this smoothed bilinear form will be spatially stable and convergent and possess three major important properties: (1) it is variationally consistent, if the solution is sought in a Hilbert space; (2) the stiffness of the discretized model will be reduced compared to the model of the finite element method (FEM) and often the exact model, which allows us to obtain upper bound solutions with respect to both the FEM solution and the exact solution; (3) the solution of the numerical method developed using the smoothed bilinear form is less insensitive to the quality of the mesh, and triangular meshes can be used perfectly without any problems. These properties have been proved, examined, and confirmed by the numerical examples. The smoothed bilinear form establishes a unified theoretical foundation for a class of smoothed Galerkin methods to analyze solid mechanics problems for solutions of special and unique properties: the node-based smoothed point interpolation method (NS-PIM), smoothed finite element method (SFEM), node-based smoothed finite element method (N-SFEM), edge-based smoothed finite element method (E-SFEM), cell-based smoothed point interpolation method (CS-PIM), etc.

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Yao, Gang, Nuno V. da Silva, Vladimir Kazei, Di Wu, and Chenhao Yang. "Extraction of the tomography mode with nonstationary smoothing for full-waveform inversion." GEOPHYSICS 84, no. 4 (July 1, 2019): R527—R537. http://dx.doi.org/10.1190/geo2018-0586.1.

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Full-waveform inversion (FWI) includes migration and tomography modes. The tomographic component of the gradient from reflection data is usually much weaker than the migration component. To use the tomography mode to fix background velocity errors, it is necessary to extract the tomographic component from the gradient. Otherwise, the inversion will be dominated by the migration mode. We have developed a method based on nonstationary smoothing to extract the tomographic component from the raw gradient. By analyzing the characteristics of the scattering angle filtering, the wavenumber of the tomographic component at a given frequency is seen to be smaller than that of the migration component. Therefore, low-wavenumber-pass filtering can be applied to extract the tomographic component. The low-wavenumber-pass smoothing filters are designed with Gaussian filters that are determined by the frequency of inversion, the model velocity, and the minimum scattering angle. Thus, this filtering is nonstationary smoothing in the space domain. Because this filtering is carried out frequency by frequency, it works naturally and efficiently for FWI based on frequency-domain modeling. Furthermore, because the maximum opening angle of the reflections in a typical acquisition geometry is much smaller than the minimum scattering angle for the tomographic component, which is generally set at 160°, there is a relatively large gap between the wavenumbers of the tomographic and migration components. In other words, the nonstationary smoothing can be applied once to a group of frequencies for time-domain FWI without leaking the migration component into the tomographic component. Analyses and numerical tests indicate that two frequency groups are generally sufficient to extract the tomographic component for the typical frequency range of time-domain FWI. The numerical tests also demonstrate that the nonstationary smoothing method is effective and efficient at extracting the tomographic component for reflection waveform inversion.

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Miyazaki, Kazuyuki, and Toshiki Iwasaki. "The Gradient Genesis of Stratospheric Trace Species in the Subtropics and around the Polar Vortex." Journal of the Atmospheric Sciences 65, no. 2 (February 1, 2008): 490–508. http://dx.doi.org/10.1175/2007jas2403.1.

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Abstract Mechanisms that control the formation and decay of meridional gradients in stratospheric trace species in the subtropics and around the polar vortex are investigated using a gradient genesis equation that uses mass-weighted isentropic zonal means. Application of this method to global nitrous oxide (N2O) data output from a global chemical transport model shows that mean vertical transport increases the meridional tracer gradient from the subtropics to midlatitudes through the shearing deformation, particularly related to overturning of the Brewer–Dobson circulation. Mean meridional transport advects the subtropical tracer gradient toward midlatitudes, while the eddy stairstep effect, steepening at the edge of the well-mixed region because of a meridional gradient in the diffusion coefficient, increases the tracer gradient in the subtropics and around the polar vortex. Mechanisms controlling the evolution of the tracer gradients in the subtropics differ between spring and autumn. The autumnal subtropical tracer gradient maximum is generated mainly from shearing deformation of the mean vertical transport, but less from mean and eddy meridional fluxes. In spring, the eddy stairstep effect also contributes to the generation of the subtropical tracer gradient maximum. Strong divergence forces stretching deformation that causes the springtime subtropical tracer gradient to decay. The gradient genesis mechanism around the Antarctic polar vortex is significantly different from that in the subtropics. Development of the tracer gradient around the Antarctic polar vortex is mostly controlled by mean meridional stretching motion in the middle stratosphere. Vertical advection and eddy smoothing effects flatten the tracer gradient as the polar vortex decays.

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Zhang, Guiyong, Da Hui, Da Li, Li Zou, Shengchao Jiang, and Zhi Zong. "A New TVD Scheme for Gradient Smoothing Method Using Unstructured Grids." International Journal of Computational Methods 17, no. 03 (November 20, 2019): 1850132. http://dx.doi.org/10.1142/s0219876218501323.

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An improved [Formula: see text]-factor algorithm for implementing total variation diminishing (TVD) scheme has been proposed for the gradient smoothing method (GSM) using unstructured meshes. Different from the methods using structured meshes, for the methods using unstructured meshes, generally the upwind point cannot be clearly defined. In the present algorithm, the value of upwind point has been successfully approximated for unstructured meshes by using the GSM with different gradient smoothing schemes, including node GSM (nGSM) midpoint GSM (mGSM) and centroid GSM (cGSM). The present method has been used to solve hyperbolic partial differential equation discontinuous problems, where three classical flux limiters (Superbee, Van leer and Minmod) were used. Numerical results indicate that the proposed algorithm based on mGSM and cGSM schemes can avoid the numerical oscillation and reduce the numerical diffusion effectively. Generally the scheme based on cGSM leads to the best performance among the three proposed schemes in terms of accuracy and monotonicity.

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Sarker, Hossain, Kamal Bechkoum, and K. K. Islam. "Optical flow for large motion using gradient technique." Serbian Journal of Electrical Engineering 3, no. 1 (2006): 103–13. http://dx.doi.org/10.2298/sjee0601103s.

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In this paper, we present the gradient-based optical flow method that estimates the two-dimensional velocity of object motion. a multi-resolution smoothing operation proposes in this paper as a pre-processing step for overcoming the difficulty of large motion estimation by gradient-based optical flow techniques. the effectiveness of the proposed method has confirmed by applying image sequence of large motion experimental results with an image sequence show a qualitative improvement.

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Xiao, Yunchen, Len Thomas, and Mark A. J. Chaplain. "Calibrating models of cancer invasion: parameter estimation using approximate Bayesian computation and gradient matching." Royal Society Open Science 8, no. 6 (June 2021): 202237. http://dx.doi.org/10.1098/rsos.202237.

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We present two different methods to estimate parameters within a partial differential equation model of cancer invasion. The model describes the spatio-temporal evolution of three variables—tumour cell density, extracellular matrix density and matrix degrading enzyme concentration—in a one-dimensional tissue domain. The first method is a likelihood-free approach associated with approximate Bayesian computation; the second is a two-stage gradient matching method based on smoothing the data with a generalized additive model (GAM) and matching gradients from the GAM to those from the model. Both methods performed well on simulated data. To increase realism, additionally we tested the gradient matching scheme with simulated measurement error and found that the ability to estimate some model parameters deteriorated rapidly as measurement error increased.

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Chen, Yuan-yuan, and Shou-qiang Du. "A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/780107.

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The nonlinear conjugate gradient method is of particular importance for solving unconstrained optimization. Finitely many maximum functions is a kind of very useful nonsmooth equations, which is very useful in the study of complementarity problems, constrained nonlinear programming problems, and many problems in engineering and mechanics. Smoothing methods for solving nonsmooth equations, complementarity problems, and stochastic complementarity problems have been studied for decades. In this paper, we present a new smoothing nonlinear conjugate gradient method for nonsmooth equations with finitely many maximum functions. The new method also guarantees that any accumulation point of the iterative points sequence, which is generated by the new method, is a Clarke stationary point of the merit function for nonsmooth equations with finitely many maximum functions.

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Wang, Sheng, George Xiangguo Xu, G. R. Liu, and Boo Cheong Khoo. "A Matrix-Free Implicit Gradient Smoothing Method (GSM) for Compressible Flows." International Journal of Aerospace and Lightweight Structures (IJALS) - 02, no. 02 (September 19, 2012): 245–80. http://dx.doi.org/10.3850/s2010428612000359.

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Narushima, Yasushi. "A smoothing conjugate gradient method for solving systems of nonsmooth equations." Applied Mathematics and Computation 219, no. 16 (April 2013): 8646–55. http://dx.doi.org/10.1016/j.amc.2013.02.060.

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Huang, Dan, and Yueming Hu. "Research on Image Smoothing Diffusion Model With Gradient and Curvature Features." IEEE Access 7 (2019): 15912–21. http://dx.doi.org/10.1109/access.2019.2892059.

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Rodríguez-Gallo, Yakdiel, Rubén Orozco-Morales, and Marlen Pérez-Díaz. "Gradient image smoothing for metal artifact reduction (GISMAR) in computed tomography." Biomedical Physics & Engineering Express 5, no. 3 (March 25, 2019): 035012. http://dx.doi.org/10.1088/2057-1976/ab0c4d.

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张, 弘强. "Dunhuang Murals’ Image Smoothing Processing Research Based on Gradient L0 Norm." Computer Science and Application 06, no. 07 (2016): 393–98. http://dx.doi.org/10.12677/csa.2016.67048.

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OMERAGIĆ, D., and P. P. SILVESTER. "THREE‐DIMENSIONAL GRADIENT RECOVERY BY LOCAL SMOOTHING OF FINITE‐ELEMENT SOLUTIONS." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 13, no. 3 (March 1994): 553–66. http://dx.doi.org/10.1108/eb010134.

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Journal articles on the topic 'Gradient Smoothing'

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