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General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems
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作者 L UO Hong-lin L UO Hui-lin 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第2期239-243,共5页
First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setti... First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT : K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems. 展开更多
关键词 two-step model general three-step model system of strongly monotonic non-linear variational inequalities projection formulas convergence of three-projection method
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Cascading multi-segment rupture process of the 2023 Turkish earthquake doublet on a complex fault system revealed by teleseismic P wave back projection method 被引量:1
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作者 Bonan Cao Zengxi Ge 《Earthquake Science》 2024年第2期158-173,共16页
In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back proj... In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks. 展开更多
关键词 2023 Turkish earthquake doublet back projection method cascading segmented rupture process coseismic triggering super-shear ruptures
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New algorithm for solving 3D incompressible viscous equations based on projection method
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作者 牛晓峰 梁伟 +4 位作者 赵宇宏 侯华 穆彦青 黄志伟 杨伟明 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2011年第8期1826-1832,共7页
A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions a... A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method. 展开更多
关键词 implicit finite difference method 3D incompressible viscous equations projection method nonparametric statistics
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基于Projection VOF方法的熔模铸造蜡模充型过程数值模拟 被引量:2
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作者 杨铭 廖敦明 +2 位作者 陈宇豪 陈涛 顾建华 《铸造》 CAS 北大核心 2023年第2期107-114,共8页
针对熔模铸造蜡模充型过程数值模拟软件自主开发,建立了流动场和温度场数学模型,采用Cross-WLF粘度模型描述蜡料的流变性能,基于Projection VOF方法进行蜡料流动过程速度场、压力场以及自由表面的求解。通过试验测量获取了K512型蜡料的... 针对熔模铸造蜡模充型过程数值模拟软件自主开发,建立了流动场和温度场数学模型,采用Cross-WLF粘度模型描述蜡料的流变性能,基于Projection VOF方法进行蜡料流动过程速度场、压力场以及自由表面的求解。通过试验测量获取了K512型蜡料的热物理性能和流变性能的相关数据,拟合得到粘度模型参数。分别在蜡料常粘度和变粘度模型两种条件下对扳机铸件蜡模充型过程进行模拟,结果表明,所建立蜡模充型过程数学模型能较好地描述蜡料的动态流变特性和传热行为。 展开更多
关键词 熔模铸造 蜡模充型 数值模拟 projection VOF方法
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Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method 被引量:16
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作者 袁驷 杜炎 +1 位作者 邢沁妍 叶康生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第10期1223-1232,共10页
The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear probl... The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation (ODE) of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach. 展开更多
关键词 NONLINEARITY finite element method (FEM) self-adaptive analysis super-convergence element energy projection (EEP)~ ordinary differential equation(ODE)
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Low side lobe pattern synthesis using projection method with genetic algorithm for truncated cone conformal phased arrays 被引量:7
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作者 Guoqi Zeng Siyin Li +1 位作者 Yan Zhang Shanwei L 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第4期554-559,共6页
A hybrid method for synthesizing antenna's three dimensional (3D) pattern is proposed to obtain the low sidelobe feature of truncated cone conformal phased arrays. In this method, the elements of truncated cone con... A hybrid method for synthesizing antenna's three dimensional (3D) pattern is proposed to obtain the low sidelobe feature of truncated cone conformal phased arrays. In this method, the elements of truncated cone conformal phased arrays are projected to the tangent plane in one generatrix of the truncated cone. Then two dimensional (2D) Chebyshev amplitude distribution optimization is respectively used in two mutual vertical directions of the tangent plane. According to the location of the elements, the excitation current amplitude distribution of each element on the conformal structure is derived reversely, then the excitation current amplitude is further optimized by using the genetic algorithm (GA). A truncated cone problem with 8x8 elements on it, and a 3D pattern desired side lobe level (SLL) up to 35 dB, is studied. By using the hybrid method, the optimal goal is accomplished with acceptable CPU time, which indicates that this hybrid method for the low sidelobe synthesis is feasible. 展开更多
关键词 conformal phased array low side lobe pattern synthe-sis projection method genetic algorithm optimization.
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Program evaluation and its application to equipment based on super-efficiency DEA and gray relation projection method 被引量:4
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作者 Linbing Tang Dong Guo +1 位作者 Jie Wu Qingmei Tan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第6期1037-1042,共6页
For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the ... For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the super-data envelopment analysis(DEA) model and the gray system theory, a new super-DEA for measuring the weight is proposed, and a gray relation projection model is established to rank the equipment programs. Finally, this approach is used to evaluate the equipment program. The results are verified valid and can provide a new way for evaluating the equipment program. 展开更多
关键词 index weight discriminate coefficient gray relation projection method program evaluation
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Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L^2 projection method 被引量:3
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作者 石东洋 裴丽芳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第7期861-874,共14页
A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the v... A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results. 展开更多
关键词 SUPERCONVERGENCE Crouzeix-Raviart type nonconforming finite element penalty scheme L^2 projection method
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Projection and Contraction Methods for Nonlinear Complementarity Problem 被引量:2
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作者 Zhao She-feng, Fei Pu-sheng College of Mathematics and Computer Science,Wuhan University,Wuhan 430072,China 《Wuhan University Journal of Natural Sciences》 EI CAS 2000年第4期391-396,共6页
We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
关键词 nonlinear complementarity problem projection and contraction method implicit method
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SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD 被引量:3
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作者 袁驷 和雪峰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第11期1461-1474,共14页
Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted ... Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach. 展开更多
关键词 finite element method (FEM) self-adaptive solution super-convergence element energy projection ordinary differential equation (ODE)
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Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method 被引量:4
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作者 王萍 张楚涵 +1 位作者 蔡思佳 李林昊 《Transactions of Tianjin University》 EI CAS 2013年第4期293-299,共7页
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad... In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000. 展开更多
关键词 matrix recovery random projection robust principal component analysis matrix completion outlier pursuit inexact augmented Lagrange multiplier method
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A class of fully third-order accurate projection methods for solving the incompressible Navier-Stokes equations 被引量:2
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作者 Yuxin Ren Yuxi Jiang +1 位作者 Miao'er Liu Hanxin Zhang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第6期542-549,共8页
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We the... In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases. 展开更多
关键词 Incompressible Navier-Stokes equations projection methods - Third-order scheme - Local truncation error
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A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems 被引量:2
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作者 Zhimin Liu Shouqiang Du Ruiying Wang 《Journal of Applied Mathematics and Physics》 2016年第6期1024-1031,共8页
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje... In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported. 展开更多
关键词 Stochastic Generalized Linear Complementarity Problems Fischer-Burmeister Function Conjugate Gradient projection method Global Convergence
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A Count Sketch Maximal Weighted Residual Kaczmarz Method with Oblique Projection for Highly Overdetermined Linear Systems 被引量:1
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作者 Peng Zhang Longyan Li Pingping Zhang 《Advances in Pure Mathematics》 2022年第4期260-270,共11页
Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczm... Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods. 展开更多
关键词 Count Sketch Oblique projection Kaczmarz method Linear System
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PROJECTION METHODS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS 被引量:1
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作者 A. Bensebah F. Dubeau J. Gelinas 《Analysis in Theory and Applications》 1997年第3期78-90,共13页
A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th... A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given. 展开更多
关键词 projection methodS AND APPROXIMATIONS FOR ORDINARY DIFFERENTIAL EQUATIONS ODE
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CONSTRUCTIONS OF BASES FOR EXTENDED OBLIQUE PROJECTION METHOD
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作者 颜世建 黄开斌 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1995年第2期176-184,共9页
In this paper,we present some sufficient conditions for constructing the bases of the left and the right spaces to ensure the feasibility of the oblique projection method and the extended oblique projection method.
关键词 OBLIQUE projection method BASES left and right SPACES LEAST-SQUARES solution.
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A NEW GRADIENT PROJECTION METHOD AND ITS CONVERGENCE
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作者 时贞军 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1995年第1期91-106,共16页
In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale... In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties. 展开更多
关键词 linear CONSTRAINED optimization problem GRADIENT projection method GLOBALCONVERGENCE SUPERLINEAR CONVERGENCE rale.
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EXTENDED OBLIQUE PROJECTION METHOD FOR GENERALIZED LEAST SQUARES PROBLEM
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作者 黄开斌 颜世建 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1994年第2期195-201,共7页
We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessar... We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessary and sufficient conditions for computing the solution or the minimum N-norm solution of the min || A x- b ||M2 have been proposed as well. 展开更多
关键词 OBLIQUE projection method GENERALIZED least SQUARES problem mini-norm least SQUARES solution GENERALIZED inverses.
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Essential consistency of pressure Poisson equation method and projection method on staggered grids
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作者 王艺 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第6期789-794,共6页
A new pressure Poisson equation method with viscous terms is established on staggered grids. The derivations show that the newly established pressure equation has the identical equation form in the projection method. ... A new pressure Poisson equation method with viscous terms is established on staggered grids. The derivations show that the newly established pressure equation has the identical equation form in the projection method. The results show that the two methods have the same velocity and pressure values except slight differences in the CPU time. 展开更多
关键词 pressure Poisson equation projection method numerical analysis staggeredgrid computational fluid dynamics
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A Modified Projection Method for Linear Feasibility Problems
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作者 Yi-Ju Wang Hong-Yu Zhang 《International Journal of Automation and computing》 EI 2009年第4期401-405,共5页
In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of th... In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance. 展开更多
关键词 Linear feasibility problem (LFP) projection method global convergence convergence rate computational experiments
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