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A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics 被引量:1
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作者 Liang Wang Xue Zhang +1 位作者 Jingjing Meng Qinghua Lei 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期2172-2183,共12页
In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a gene... In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics. 展开更多
关键词 Particle finite element method Nodal integration Dynamic saturated media Second-order cone programming(SOCP)
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Three-dimensional Simulation of Reverberation Chamber Using Finite-element Time-domain Method 被引量:1
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作者 DU Lei WANG Song +2 位作者 CUI Yaozhong WANG Qingguo PAN Yun 《高电压技术》 EI CAS CSCD 北大核心 2013年第12期2889-2893,共5页
关键词 三维模拟 时域法 有限元 混响室 几何建模 标准偏差 雷达散射截面 低频响应
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Finite difference time domain method forward simulation of complex geoelectricity ground penetrating radar model 被引量:5
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作者 戴前伟 冯德山 何继善 《Journal of Central South University of Technology》 EI 2005年第4期478-482,共5页
The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of c... The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model. 展开更多
关键词 ground penetrating radar finite difference time domain method forward simulation ideal frequency dispersion relationship
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Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients 被引量:2
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作者 Andrew Lundberg Pengtao Sun +1 位作者 Cheng Wang Chen-song Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2019年第4期35-62,共28页
The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully disc... The distributed Lagrange multiplier/fictitious domain(DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients.The semi-and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface,where the arbitrary Lagrangian-Eulerian(ALE)technique is employed to deal with the moving and immersed subdomain.Stability and optimal convergence properties are obtained for both schemes.Numerical experiments are carried out for different scenarios of jump coefficients,and all theoretical results are validated. 展开更多
关键词 TRANSIENT STOKES interface problem JUMP COEFFICIENTS DISTRIBUTED LAGRANGE multiplier fictitious domain method mixed finite element an optimal error estimate stability
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INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS 被引量:1
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作者 应隆安 《Acta Mathematica Scientia》 SCIE CSCD 2001年第4期440-452,共13页
The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite n... The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given. 展开更多
关键词 finite element method infinite element method unbounded domain multiply connected domain
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Mixed time discontinuous space-time finite element method for convection diffusion equations 被引量:1
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作者 刘洋 李宏 何斯日古楞 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第12期1579-1586,共8页
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order... A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method. 展开更多
关键词 convection diffusion equations mixed finite element method time discontinuous space-time finite element method CONVERGENCE
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Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar 被引量:1
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作者 Zhi Zhang Honghua Wang +2 位作者 Minling Wang Xi Guo Guihong Guo 《Journal of Applied Mathematics and Physics》 2019年第5期1077-1096,共20页
As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order elec... As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures. 展开更多
关键词 Non-Split Perfectly Matched Layer (NPML) Ground PENETRATING Radar (GPR) SECOND Order Wave Equation finite element time domain (FETD)
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THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS 被引量:5
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作者 LI Hong(李宏) +1 位作者 LIU Ru-xun(刘儒勋) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第6期687-700,共14页
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference ... Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L-infinity (L-2) norm, that is maximum-norm in time, L-2-norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained. 展开更多
关键词 semi-linear parabolic equations space-time finite element method existence and uniquess error estimate
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A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations 被引量:1
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作者 陈豫眉 谢小平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第7期861-874,共14页
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretizatio... A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming (P1)2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms. 展开更多
关键词 streamline diffusion method finite difference method nonconforming finite element method time-dependent linearized Navier-Stokes equations error estimate
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Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method 被引量:1
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作者 马秀荣 徐林 +1 位作者 常世元 张双根 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第4期190-197,共8页
This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the... This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo's amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm^(3+):YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp(α'L),which is previously employed to describe the relationship between echo's efficiency and thickness,should be modified as 1.3 · 0.09 exp(2.4 ·α'L) with the propagation of echo considered. 展开更多
关键词 three-pulse photon echo Maxwell-Bloch equations finite-difference time-domain method
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SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION
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作者 汤琼 陈传淼 刘罗华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第3期335-340,共6页
Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved thro... Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory. 展开更多
关键词 nonlinear SchrSdinger equation space-time finite element method energy integration CONSERVATION
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Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method
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作者 林治家 由小川 庄茁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第5期539-552,共14页
Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It lead... Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures. 展开更多
关键词 goal-oriented error estimation finite element method (FEM) direct-solutionsteady-state analysis frequency domain
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Determination of the Minimum Testing Time for Wireline Formation Testing with the Finite Element Method
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作者 Hu Falong Xiao Lizhi +1 位作者 Zhang Yuanzhong Wang Chengwei 《Petroleum Science》 SCIE CAS CSCD 2006年第1期39-44,共6页
The wireline formation tester (WFT) is an important tool for formation evaluation, such as calculating the formation pressure and permeability, identifying the fluid type, and determining the interface between oil a... The wireline formation tester (WFT) is an important tool for formation evaluation, such as calculating the formation pressure and permeability, identifying the fluid type, and determining the interface between oil and water. However, in a low porosity and low permeability formation, the supercharge pressure effect exists, since the mudcake has a poor sealing ability. The mudcake cannot isolate the hydrostatic pressure of the formation around the borehole and the mud seeps into the formations, leading to inaccurate formation pressure measurement. At the same time, the tool can be easily stuck in the low porosity/low permeability formation due to the long waiting and testing time. We present a method for determining the minimum testing time for the wireline formation tester. The pressure distribution of the mudcake and the formation were respectively calculated with the finite element method (FEM). The radius of the influence of mud pressure was also computed, and the minimum testing time in low porosity/low permeability formations was determined within a range of values for different formation permeabilities. The determination of the minimum testing time ensures an accurate formation pressure measurement and minimizes possible accidents due to long waiting and testing time. 展开更多
关键词 Wireline formation tester the minimum testing time the finite element method
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A TIME DOMAIN BOUNDARY ELEMENT METHOD FOR WATER-SOLID IMPACT ANALYSIS
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作者 Huang, YY Yue, DY Qian, Q 《Acta Mechanica Solida Sinica》 SCIE EI 1995年第4期337-348,共12页
A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding tim... A reciprocal theorem of dynamics for potential flow problems is first derived by means of the Laplace transform in which the compressibility of water is taken into account. Based on this theorem, the corresponding time-space boundary integral equation: is obtained. Then, a set of time domain boundary element equations with recurrence form is immediately formulated through discretization in both time and boundary. After having carried out the numerical calculation two solutions are found in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impact on the surface of a half-space fluid. The results show that the present method is more efficient than the previous ones. 展开更多
关键词 fluid-structure impact potential flow problem time domain boundary element method interaction between fluid and structure
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Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method 被引量:1
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作者 窦虎 马红梅 孙玉宝 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第9期117-121,共5页
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ... The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell's equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change. 展开更多
关键词 finite-difference time-domain method blue phase liquid crystal display in-plane switching convergence effect
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On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions
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作者 Konstantin Kazakov 《American Journal of Computational Mathematics》 2013年第2期104-109,共6页
This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel ... This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions. 展开更多
关键词 Soil-Structure Interaction Wave Propagation INfinite elements finite element method BESSEL Functions DUHAMEL INTEGRAL
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Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method
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作者 Huwaida K.Elgweri Amal Hamed Mohamed Mansor 《Journal of Physical Science and Application》 2022年第1期12-18,共7页
The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method i... The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique. 展开更多
关键词 finite difference time domain method diffusion equation separation of variables method finite well potential Schrödinger equation
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Aerodynamic Design of Airfoils Based on Variable-Domain Variational Finite Element Method
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作者 陈池 刘高联 《Journal of Shanghai University(English Edition)》 CAS 2005年第3期210-215,共6页
Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational ... Designing airfoils according to given pressure (or velocity) distribution is one kind of free boundary problems. Free boundary condition can be coupled with the flow governing equations by variable-domain variational calculus, which makes it possible to calculate simultaneously the flow field and the free boundary. An accurate deduction of the variable-domain variational principles is taken herein to design airfoils in compressible and incompressible flows. Furthermore, two grid types (H and O) are used in the calculation with better results for the O-type grid. It is shown that convergence is accelerated and good results can be obtained even if the initial guessed airfoil shape is a triangle, demonstrating the strong adaptability of this method. 展开更多
关键词 inverse design finite element method variable-domain variational principle.
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An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme
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作者 魏晓琨 邵维 +2 位作者 石胜兵 张勇 王秉中 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第7期74-82,共9页
An efficient conformal locally one-dimensional finite-difference time-domain(LOD-CFDTD) method is presented for solving two-dimensional(2D) electromagnetic(EM) scattering problems. The formulation for the 2D tra... An efficient conformal locally one-dimensional finite-difference time-domain(LOD-CFDTD) method is presented for solving two-dimensional(2D) electromagnetic(EM) scattering problems. The formulation for the 2D transverse-electric(TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit(ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field(TF/SF) boundary and the perfectly matched layer(PML), the radar cross section(RCS) of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method. 展开更多
关键词 conformal scheme locally one-dimensional(LOD) finite-difference time-domain(FDTD) method numerical dispersion unconditional stab
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A Consistent Time Level Implementation Preserving Second-Order Time Accuracy via a Framework of Unified Time Integrators in the Discrete Element Approach
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作者 Tao Xue YazhouWang +3 位作者 Masao Shimada David Tae Kumar Tamma Xiaobing Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第3期1469-1487,共19页
In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presente... In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order. 展开更多
关键词 Computational dynamics time integration Discrete element method(DEM)
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