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Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Zeyue Zhang Boyu Chen Zhijun Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第9期2707-2728,共22页
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t... Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions. 展开更多
关键词 Peridynamic differential operator finite difference method STABILITY transient heat conduction problem
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ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS 被引量:3
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作者 白中治 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 1996年第2期228-233,共6页
Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate o... Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated. 展开更多
关键词 LINEAR complementarity PROBLEM projected ITERATIon method MonOTonE convergence.
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EFFECTIVE NUMERICAL METHODS FOR ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION 被引量:2
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作者 Wang Xucheng Chang Liangming Cen Zhangzhi (Department of Engineering Mechanics,Tsinghua University) 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1990年第4期349-356,共8页
Several effective numerical methods for solving the elasto-plastic contact problems with friction are pres- ented.First,a direct substitution method is employed to impose the contact constraint conditions on condensed... Several effective numerical methods for solving the elasto-plastic contact problems with friction are pres- ented.First,a direct substitution method is employed to impose the contact constraint conditions on condensed finite ele- ment equations,thus resulting in a reduction by half in the dimension of final governing equations.Second,an algorithm composed of contact condition probes and elasto-plastic iterations is utilized to solve the governing equation,which distinguishes two kinds of nonlinearities,and makes the solution unique.In addition,Positive-Negative Sequence Modifica- tion Method is used to condense the finite element equations of each substructure and an analytical integration is intro- duced to determine the elasto-plastic status after each time step or each iteration,hence the computational efficiency is en- hanced to a great extent.Finally,several test and practical examples are pressented showing the validity and versatility of these methods and algorithms. 展开更多
关键词 ELASto-PLASTICITY contact problem finite element method
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The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrdinger Equations 被引量:2
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作者 LI YUAN MA FU-MING 《Communications in Mathematical Research》 CSCD 2010年第4期321-336,共16页
This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the sca... This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of (A* A) ^1/4 and G which maps more general incident fields than plane waves into the scattering amplitude coincide.As an application we characterize the support of the potential using only the spectral data of the operator A. 展开更多
关键词 factorization method inverse scattering Schrdinger equation interior transmission problem
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A Mathematical Model to Solve Bio-Heat Transfer Problems through a Bio-Heat Transfer Equation with Quadratic Temperature-Dependent Blood Perfusion under a Constant Spatial Heating on Skin Surface 被引量:1
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作者 Emmanuel Kengne Idir Mellal +1 位作者 Mariem Ben Hamouda Ahmed Lakhssassi 《Journal of Biomedical Science and Engineering》 2014年第9期721-730,共10页
We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method w... We consider the one-dimensional bio-heat transfer equation with quadratic temperature-dependent blood perfusion, which governs the temperature distribution inside biological tissues. Using an extended mapping method with symbolic computation, we obtain the exact analytical thermal traveling wave solution, which describes the non-uniform temperature distribution inside the bodies. The found exact solution is used to investigate the temperature distribution in the tissues. It is found that the surrounding medium with higher temperature does not necessarily imply that the tissue will quickly (after a short duration of heating process) reach the desired temperature. It is also found that increased perfusion causes a decline in local temperature. 展开更多
关键词 Bio-Heat Transfer problems Pennes Bio-Heat Model TEMPERATURE-DEPENDENT Blood PERFUSIon Thermal Therapy Extended Mapping Method
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Newton-type methods and their modifications for inverse heat conduction problems
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作者 康传刚 孟泽红 贺国强 《Journal of Shanghai University(English Edition)》 CAS 2010年第3期196-200,共5页
This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several mo... This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs. 展开更多
关键词 nonlinear inverse problem inverse heat conduction problem Newton-Tikhonov method Newton-implicit iterative method modification
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A note on a family of proximal gradient methods for quasi-static incremental problems in elastoplastic analysis
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作者 Yoshihiro Kanno 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2020年第5期315-320,共6页
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical ... Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities. 展开更多
关键词 Elastoplastic analysis Incremental problem Nonsmooth convex optimization First-order optimization method Proximal gradient method
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NUMERICAL RESOLVENT METHODS FOR CONSTRAINED PROBLEMS IN MECHANICS
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作者 Gonzalo Alduncin 《Analysis in Theory and Applications》 1996年第4期1-25,共25页
Resolvent methods are presented for generating systematically iterative numerical algorithms for constrained problems in mechanics.The abstract framework corresponds to a general mixed finite element subdif-ferential ... Resolvent methods are presented for generating systematically iterative numerical algorithms for constrained problems in mechanics.The abstract framework corresponds to a general mixed finite element subdif-ferential model,with dual and primal evolution versions,which is shown to apply to problems of fluid dynamics,transport phenomena and solid mechanics,among others.In this manner,Uzawa's type methods and penalization-duality schemes,as well as macro-hybrid formulations,are generalized to non necessarily potential nanlinear mechanical problems. 展开更多
关键词 PRO this NUMERICAL REsolveNT methods FOR ConSTRAINED problems IN MECHANICS
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Adhering to Opening-up is the Key to Solve Sino-US Economic and Trade Problems
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作者 Wang Huiyao 《International Understanding》 2019年第3期32-34,共3页
The new round of Sino-US high-level economic and trade consultations has been concluded.This is the 13th round of negotiations since the wide acceleration of economic and trade frictions between China and US.
关键词 Opening-up the KEY solve Sino-US EConOMIC Trade problems
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Analysis of Existing Problems and Treatment Methods of Urban Environmental Monitoring
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作者 Zhang Qiandong Song Xin 《Journal of Environmental Science and Engineering(A)》 2022年第2期49-54,共6页
With the rapid development of the city,the concept of ecological environment has been integrated into everyone’s heart.In the new era,people also have higher requirements for the quality of living environment.However... With the rapid development of the city,the concept of ecological environment has been integrated into everyone’s heart.In the new era,people also have higher requirements for the quality of living environment.However,at this stage,with the development of urbanization and industrialization,the problem of environmental pollution has become more and more serious.Therefore,we must do a good job in urban environmental monitoring,pay attention to the protection of urban environment,design and implement effective governance methods,so as to improve the quality of environmental governance.This article analyzes the problems in urban environmental monitoring,and formulates reasonable treatment methods and suggestions. 展开更多
关键词 Urban environmental monitoring problems governance methods ANALYSIS
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How to Solve Percentage Problems?
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作者 张丽莉 《疯狂英语(理论版)》 2019年第1期45-48,共4页
Some of the primary school students can solve percentage problems written in Chinese but fail to solve them written in English. Why?Is bilingual maths more diffi cult than Chinese maths? The answer is 'No'.The... Some of the primary school students can solve percentage problems written in Chinese but fail to solve them written in English. Why?Is bilingual maths more diffi cult than Chinese maths? The answer is 'No'.The main reason is that they might not know well about the formula of percentage and the English expressions of percentage. 展开更多
关键词 solve PERCENTAGE problems PERCENTAGE
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To Solve the Problems of English Teaching in China: A Comprehensive Literature Review
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作者 郭思含 《海外英语》 2019年第5期242-244,共3页
English education in China has its problems due to its history and teaching environment,such as deficiency of communication purpose,insufficiency of teaching on oral expression and so on.Consequently,to solve the prob... English education in China has its problems due to its history and teaching environment,such as deficiency of communication purpose,insufficiency of teaching on oral expression and so on.Consequently,to solve the problems of English teaching in China seems necessary.Therefore,the solutions as the changes of policy,updated teaching methods,improvement of teacher’s skills on teaching and diverse ways of teaching should be pointed out. 展开更多
关键词 LITERATURE review problems solving English LANGUAGE teaching
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Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements 被引量:4
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作者 B. Kanber O. Yavuz Bozkurt 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第4期355-365,共11页
In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based... In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results. 展开更多
关键词 Finite element method Transition plate elements Elasto-plastic analysis. Plate bending problems
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A Nonmonotone Filter Method for Minimax Problems 被引量:2
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作者 Qi Zhao Nan Guo 《Applied Mathematics》 2011年第11期1372-1377,共6页
In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP... In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function as a merit function and the nonmonotone filter to improve the effect of the algorithm. Under some mild conditions, we prove the global convergence. 展开更多
关键词 MINIMAX PROBLEM NonMonOTonE GLOBAL ConVERGENCE FILTER methods
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A mixed Newton-Tikhonov method for nonlinear ill-posed problems 被引量:1
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作者 康传刚 贺国强 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第6期741-752,共12页
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical p... Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs. 展开更多
关键词 nonlinear ill-posed problem inverse heat conduction problem mixedNewton-Tikhonov method ConVERGENCE stability
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EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS 被引量:2
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作者 Liu Yongjin Zhang Liwei Liu Meijiao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第2期245-252,共8页
The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity proble... The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0. 展开更多
关键词 symmetric cone complementarity problem smoothing function Euclidean Jordan algebra non-interior continuation method
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AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS 被引量:1
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作者 Shuqiang Wang Roman Samulyak Tongfei Guo 《Acta Mathematica Scientia》 SCIE CSCD 2010年第2期499-521,共23页
The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella (1998, J. Comput. Phys. 147, 60) has been extended for ellipti... The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella (1998, J. Comput. Phys. 147, 60) has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems. 展开更多
关键词 embedded boundary method elliptic interface problem front tracking Ste-fan problem
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Highly Accurate Golden Section Search Algorithms and Fictitious Time Integration Method for Solving Nonlinear Eigenvalue Problems
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作者 Chein-Shan Liu Jian-Hung Shen +1 位作者 Chung-Lun Kuo Yung-Wei Chen 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1317-1335,共19页
This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve... This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency. 展开更多
关键词 Nonlinear eigenvalue problem quadratic eigenvalue problem two new merit functions golden section search algorithm fictitious time integration method
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Preconditioned iterative methods for solving weighted linear least squares problems 被引量:2
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作者 沈海龙 邵新慧 张铁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第3期375-384,共10页
A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems... A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation (GAOR) methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment. 展开更多
关键词 PREConDITIonER generalized accelerated overrelaxation (GAOR) method weighted linear least squares problem ConVERGENCE
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Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems
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作者 Chein-Shan Liu Chung-Lun Kuo Chih-Wen Chang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第6期3189-3208,共20页
To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection techniq... To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11). 展开更多
关键词 Laplace equation nonharmonic boundary value problem Ill-posed problem maximal projection optimal shape factor and fictitious radius optimal MQ-RBF optimal polynomial method
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