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A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems 被引量:1
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作者 Jufeng Wang Yong Wu +1 位作者 Ying Xu Fengxin Sun 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第4期341-356,共16页
By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is propose... By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability. 展开更多
关键词 dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method interpolating variational multiscale element-free Galerkin(VMIEFG)method dimension splitting method singularly perturbed convection-diffusion problems
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NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS 被引量:5
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作者 袁益让 杨青 +1 位作者 李长峰 孙同军 《Acta Mathematica Scientia》 SCIE CSCD 2017年第1期259-279,共21页
Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi... Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device. 展开更多
关键词 three dimensional transient behavior of heat conduction problem mixed finitevolume element modified upwind fractional step difference second-order error
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The dimension split element-free Galerkin method for three-dimensional potential problems 被引量:4
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作者 Z.J.Meng H.Cheng +1 位作者 L.D.Ma Y.M.Cheng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第3期462-474,共13页
This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-d... This paper presents the dimension split element-free Galerkin (DSEFG) method for three-dimensional potential problems, and the corresponding formulae are obtained. The main idea of the DSEFG method is that a three-dimensional potential problem can be transformed into a series of two-dimensional problems. For these two-dimensional problems, the improved moving least-squares (IMLS) approximation is applied to construct the shape function, which uses an orthogonal function system with a weight function as the basis functions. The Galerkin weak form is applied to obtain a discretized system equation, and the penalty method is employed to impose the essential boundary condition. The finite difference method is selected in the splitting direction. For the purposes of demonstration, some selected numerical examples are solved using the DSEFG method. The convergence study and error analysis of the DSEFG method are presented. The numerical examples show that the DSEFG method has greater computational precision and computational efficiency than the IEFG method. 展开更多
关键词 dimension split method Improved moving least-squares (IMLS) approximation Improved element-free Galerkin (IEFG) method Finite difference method (FDM) dimension split element-free Galerkin (DSEFG) method Potential problem
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Two kinds of contact problems in three-dimensional icosahedral quasicrystals 被引量:10
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作者 Xuefen ZHAO Xing LI Shenghu DING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第12期1569-1580,共12页
Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional (3D) icosahedral quasicrystals are dis- cussed by a complex variable function method. For th... Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional (3D) icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified. 展开更多
关键词 three-dimensional (3D) icosahedral quasicrystal Riemann-Hilbert problem contact problem SINGULARITY complex variable function method
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Recursive super-convergence computation for multi-dimensional problems via one-dimensional element energy pro jection technique 被引量:11
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作者 Si YUAN Yue WU Qinyan XING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第7期1031-1044,共14页
This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method (FEM) by recursive application of the one-dimensional (1D) element energy pro... This paper presents a strategy for computation of super-convergent solutions of multi-dimensional problems in the finite element method (FEM) by recursive application of the one-dimensional (1D) element energy projection (EEP) technique. The main idea is to conceptually treat multi-dimensional problems as generalized 1D problems, based on which the concepts of generalized 1D FEM and its consequent EEP formulae have been developed in a unified manner. Equipped with these concepts, multi-dimensional problems can be recursively discretized in one dimension at each step, until a fully discretized standard finite element (FE) model is reached. This conceptual dimension-by- dimension (D-by-D) discretization procedure is entirely equivalent to a full FE discretization. As a reverse D-by-D recovery procedure, by using the unified EEP formulae together with proper extraction of the generalized nodal solutions, super-convergent displacements and first derivatives for two-dimensional (2D) and three-dimensional (3D) problems can be obtained over the domain. Numerical examples of 3D Poisson's equation and elasticity problem are given to verify the feasibility and effectiveness of the proposed strategy. 展开更多
关键词 three-dimensional(3D)problem generalized one-dimensional(1D)finiteelement method (FEM) dimension-by-dimension(D-by-D) super-convergence elementenergy projection(EEP)
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TWO-DIMENSIONAL RIEMANN PROBLEMS:FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS 被引量:4
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作者 李杰权 盛万成 +1 位作者 张同 郑玉玺 《Acta Mathematica Scientia》 SCIE CSCD 2009年第4期777-802,共26页
In this paper we survey the authors' and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s... In this paper we survey the authors' and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models. 展开更多
关键词 two-dimensional Riemann problem compressible Euler equation reflection of shocks interaction of rarefaction waves delta-shocks
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Solution Method for Singular Initial Value Problems of One-dimensional Steady Transonic Flow in a Dual-mode Scramjet 被引量:1
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作者 崔涛 于达仁 鲍文 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第2期97-101,共5页
Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts f... Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet. 展开更多
关键词 SCRAMJET one-dimensional analysis transonic flow singular initial value problem
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Boundary Value Problems for Nonlinear Elliptic Equations of Second Order in High Dimensional Domains
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作者 Guochun Wen Dechang Chen 《Applied Mathematics》 2013年第12期1651-1657,共7页
This paper mainly concerns oblique derivative problems for nonlinear nondivergent elliptic equations of second order with measurable coefficients in a multiply connected domain. Under certain condition, we derive a pr... This paper mainly concerns oblique derivative problems for nonlinear nondivergent elliptic equations of second order with measurable coefficients in a multiply connected domain. Under certain condition, we derive a priori estimates of solutions. By using these estimates and the fixed-point theorem, we prove the existence of solutions. 展开更多
关键词 blique DERIVATIVE problems Nonlinear ELLIPTIC EQUATIONS High dimensional DOMAINS
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A branch-and-bound algorithm for multi-dimensional quadratic 0-1 knapsack problems 被引量:2
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作者 孙娟 盛红波 孙小玲 《Journal of Shanghai University(English Edition)》 CAS 2007年第3期233-236,共4页
In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding ... In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems. 展开更多
关键词 multi-dimensional quadratic 0-1 knapsack problem branch-and-bound method Lagrangian relaxation outer approximation surrogate constraint.
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Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation 被引量:1
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作者 黄俊杰 阿拉坦仓 王华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第8期1039-1048,共10页
This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe... This paper proposes an eigenfunction expansion method to solve twodimensional (2D) elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method. 展开更多
关键词 eigenfunction expansion method two-dimensional (2D) elasticity problem upper triangular differential system general solution
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Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle
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作者 Shuai Wang 《Journal of Applied Mathematics and Physics》 2023年第4期1029-1035,共7页
In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilin... In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem. 展开更多
关键词 High-dimensional Axisymmetric Hyperbolic Equations Supersonic Flow in a Nozzle Local Solutions to Boundary Value problems of Quasilinear Hyperbolic Equations
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Exponential Convergence of Finite-dimensional Approximations to Linear Bond-based Peridynamic Boundary Value Problems
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作者 WU HAO 《Communications in Mathematical Research》 CSCD 2018年第3期278-288,共11页
In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity ass... In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature. 展开更多
关键词 PERIDYNAMICS exponential convergence nonlocal boundary value problem analytic function finite-dimensional approximation
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Existence Results for m-Point Boundary Value Problem at Resonance with One-dimensional p-Laplacian
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作者 沈春芳 杨刘 刘锡平 《Northeastern Mathematical Journal》 CSCD 2008年第2期129-142,共14页
By using Mawhin's continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main... By using Mawhin's continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper. 展开更多
关键词 boundary value problem one-dimensional p-Laplacian RESONANCE coincidence degree
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Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method
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作者 胡杨凡 王彪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第12期1535-1552,共18页
Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-... Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section. 展开更多
关键词 SCATTERING piezoelectric/piezomagnetic material polarization method dynamic Green's function two-dimensional problem Radon transform anisotropic material
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Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation
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作者 额布日力吐 阿拉坦仓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第2期223-232,共10页
This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem... This paper studies the eigenfunction expansion method to solve the two dimensional (2D) elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example. 展开更多
关键词 eigenfunction expansion method two-dimensional (2D) elasticity problem upper triangular operator matrix general solution
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Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing
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作者 李方方 刘静 乐恺 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第1期63-72,共10页
Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green func... Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change. 展开更多
关键词 three-dimensional phase change heat transfer problem CRYOSURGERY CRYOPRESERVATION moving heat source model bioheat transfer Green's function analytical solution
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THE RIEMANN PROBLEM FOR A TWO-DIMENSIONAL HYPERBOLIC SYSTEM OF CONSERVATION LAWS WITH NON-CLASSICAL SHOCK WAVES
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作者 胡家信 《Acta Mathematica Scientia》 SCIE CSCD 1998年第1期45-56,共12页
The Riemann problem for a two-dimensional 2 x 2 nonstrictly hyperbolic system of nonlinear conservation laws has been solved thoroughly for any given initial data which are constant in each quadrant. The non-classical... The Riemann problem for a two-dimensional 2 x 2 nonstrictly hyperbolic system of nonlinear conservation laws has been solved thoroughly for any given initial data which are constant in each quadrant. The non-classical shockwaves, which are labelled as delta-shock waves, appear in some solutions. The solutions have been obtained are not unique. Due to the specific property of the system considered, there are no rarefaction waves in solution. This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions. 展开更多
关键词 Riemann problem two-dimensional hyperbolic system non-classical wave
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Interactions of penny-shaped cracks in three-dimensional solids 被引量:2
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作者 Shige Zhan Tzuchiang Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2006年第4期341-353,共13页
The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped i... The interaction of arbitrarily distributed penny-shaped cracks in three-dimensional solids is analyzed in this paper. Using oblate spheroidal coordinates and displacement functions, an analytic method is devel- oped in which the opening and the sliding displacements on each crack surface are taken as the basic unknown functions. The basic unknown functions can be expanded in series of Legendre polynomials with unknown coefficients. Based on superposition technique, a set of governing equations for the unknown coefficients are formulated from the traction free conditions on each crack surface. The boundary collocation procedure and the average method for crack-surface tractions are used for solving the governing equations. The solution can be obtained for quite closely located cracks. Numerical examples are given for several crack problems. By comparing the present results with other existing results, one can conclude that the present method provides a direct and efficient approach to deal with three-dimensional solids containing multiple cracks. 展开更多
关键词 Three-dimensional problem Penny-shaped cracks INTERACTION
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Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints 被引量:3
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作者 Ziyao XU Qi WANG Qingyun WANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2017年第12期1733-1752,共20页
Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction ... Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem (NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a con- straint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects. 展开更多
关键词 non-smooth dynamics nonholonomic constraint Coulomb dry friction two-dimensional friction nonlinear complementarity problem (NCP)
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Guckenheimer structure of solution of Riemann problem with four pieces of constants in two space dimensions for scalar conservation laws 被引量:2
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作者 张华 盛万成 《Journal of Shanghai University(English Edition)》 CAS 2006年第4期305-307,共3页
By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which invo... By using the generalized characteristic analysis method, the two-dimensional four-wave Riemann problem for scalar conservation laws, which is nonconvex along the y direction, was studied. Riemann solutions, which involve the Guckenheimer structure, were constructed. 展开更多
关键词 two-dimensional Riemann problem scalar conservation laws generalized characteristic analysis method Guckenheimer structure.
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