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Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems
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作者 朱贝贝 纪伦 +1 位作者 祝爱卿 唐贻发 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第2期60-79,共20页
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on ex... We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit,K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original phase space to several copies of the phase space and imposing a mechanical restraint on the copies of the phase space. Explicit K-symplectic methods are constructed for two non-canonical Hamiltonian systems. Numerical tests show that the proposed methods exhibit good numerical performance in preserving the phase orbit and the energy of the system over long time, whereas higher order Runge–Kutta methods do not preserve these properties. Numerical tests also show that the K-symplectic methods exhibit better efficiency than that of the same order implicit symplectic, explicit and implicit symplectic methods for the original nonseparable non-canonical systems. On the other hand, the fourth order K-symplectic method is more efficient than the fourth order Yoshida’s method, the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om explicit K-symplectic methods for the extended phase space Hamiltonians, but less efficient than the the optimized partitioned Runge–Kutta and Runge–Kutta–Nystr ¨om extended phase space symplectic-like methods with the midpoint permutation. 展开更多
关键词 non-canonical Hamiltonian systems NONSEPARABLE explicit K-symplectic methods splitting method
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Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Kunfeng Liang Zhijun Liu Xinru Bao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期3033-3049,共17页
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna... Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed. 展开更多
关键词 Population balance equation CRYSTALLIZATION peridynamic differential operator Euler’s first-order explicit method
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An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations
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作者 Huang Huan Li Yingxiong Li Yuyu 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2024年第3期677-690,共14页
An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are as... An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems. 展开更多
关键词 nonstationary random vibration plastic hinge equivalent linearization method explicit time-domain method parallel computation
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OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD 被引量:6
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作者 X. G. Bao D. N. He +2 位作者 D. Lu C. X. Li J. L. Cheng and J. Y. Jiang( 1) National Mold and Dies CAD Engineering Research Center, Shanghai 200030, China 2) Shanghai Volkswagen Automotive Company Ltd.(SVW), Shanghai 201805, China) 《Acta Metallurgica Sinica(English Letters)》 SCIE EI CAS CSCD 2000年第1期387-393,共7页
Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this... Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained. 展开更多
关键词 dynamic explicit finite element method autobody panel OPTIMIZATION stamping process
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A family of explicit algorithms for general pseudodynamic testing 被引量:2
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作者 Shuenn-Yih Chang Chi-Wei Hsu 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2011年第1期51-64,共14页
A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a... A new family of explicit pseudodynamic algorithms is proposed for general pseudodynamic testing. One particular subfamily seems very promising for use in general pseudodynamic testing since the stability problem for a structure does not need to be considered. This is because this subfamily is unconditionally stable for any instantaneous stiffness softening system, linear elastic system and instantaneous stiffness hardening system that might occur in the pseudodynamic testing of a real structure. In addition, it also offers good accuracy when compared to a general second-order accurate method for both linear elastic and nonlinear systems. 展开更多
关键词 pseudodynamic test explicit method unconditional stability dominant mode structural dynamics instantaneous degree of nonlinearity
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A fast explicit finite difference method for determination of wellhead injection pressure 被引量:2
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作者 白冰 李小春 +2 位作者 刘明泽 石露 李琦 《Journal of Central South University》 SCIE EI CAS 2012年第11期3266-3272,共7页
A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditiona... A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected. 展开更多
关键词 wellhead pressure injection pressure bottom-hole pressure fast explicit finite difference method
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An explicit finite volume element method for solving characteristic level set equation on triangular grids 被引量:1
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作者 Sutthisak Phongthanapanich Pramote Dechaumphai 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第6期911-921,共11页
Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow pheno... Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme. 展开更多
关键词 Keywords Characteristic level set equation - Finite volume element method explicit method Triangular grid Twophase incompressible flow
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Explicit concomitance of implicit method to solve vibration equation
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作者 Li, Changqing Jiang, Lizhong 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2012年第2期269-272,共4页
It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concom... It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method,which is called the concomitant explicit method.The constant acceleration method's concomitant explicit method was used as an example and is described in detail in this paper.The relationship between the implicit method and explicit method is defined,which provides some guidance about how to create a new explicit method that has high precision and computational efficiency. 展开更多
关键词 dynamic analysis explicit method implicit method structural dynamics
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Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
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作者 Hendrik Ranocha Lisandro Dalcin +1 位作者 Matteo Parsani David I.Ketcheson 《Communications on Applied Mathematics and Computation》 2022年第4期1191-1228,共38页
We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusi... We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications. 展开更多
关键词 explicit Runge-Kutta methods Step size control Compressible Euler equations Compressible Navier-Stokes equations hp-adaptive spatial discretizations
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An explicit finite element method for dynamic analysis in three-medium coupling system and its application
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作者 赵成刚 李伟华 +1 位作者 王进廷 李亮 《Acta Seismologica Sinica(English Edition)》 CSCD 2003年第3期272-282,共11页
In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on ... In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given. 展开更多
关键词 fluid saturated porous medium-elastic single-phase medium-ideal fluid medium coupled system dynamic response analysis explicit finite element method
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Sheet Metal Forming Simulation and Its Application in Stamping Process of Automobile Panels 被引量:4
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作者 张扬 张连洪 +1 位作者 李双义 王洪志 《Transactions of Tianjin University》 EI CAS 2002年第4期269-272,共4页
The paper starts with a brief overview to the necessity of sheet metal forming simulation and the complexity of automobile panel forming, then leads to finite element analysis (FEA) which is a powerful simulation too... The paper starts with a brief overview to the necessity of sheet metal forming simulation and the complexity of automobile panel forming, then leads to finite element analysis (FEA) which is a powerful simulation tool for analyzing complex three-dimensional sheet metal forming problems. The theory and features of the dynamic explicit finite element methods are introduced and the available various commercial finite element method codes used for sheet metal forming simulation in the world are discussed,and the civil and international status quo of automobile panel simulation as well. The front door outer panel of one certain new automobile is regarded as one example that the dynamic explicit FEM code Dynaform is used for the simulation of the front door outer panel forming process. Process defects such as ruptures are predicted. The improving methods can be given according to the simulation results. Foreground of sheet metal forming simulation is outlined. 展开更多
关键词 finite element analysis dynamic explicit methods sheet metal forming finite element method codes automobile panel computer simulation APPLICATION
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Dynamic analysis of dam-reservoir-foundation interaction using finite difference technique 被引量:2
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作者 M.Abdollahi R.Attarnejad 《Journal of Central South University》 SCIE EI CAS 2012年第5期1399-1410,共12页
Time domain dynamic analysis of inclined dam-reservoir-foundation interaction was conducted using finite difference method (FDM). The Timoshenko beam theory and the Euler-Bemoulli beam theory were implemented to dra... Time domain dynamic analysis of inclined dam-reservoir-foundation interaction was conducted using finite difference method (FDM). The Timoshenko beam theory and the Euler-Bemoulli beam theory were implemented to draw out governing equation of beam. The interactions between the dam and the soil were modeled by using a translational spring and a rotational spring. A Sommerfeld's radiation condition at the infinity boundary of the fluid domain was adopted. The effects of the reservoir bottom absorption and surface waves on the dam-reservoir-foundation interaction due to the earthquake were studied. To avoid the instability of solution, a semi-implicit scheme was used for the discretization of the governing equation of dam and an explicit scheme was used for the discretization of the governing equation of fluid. The results show that as the slope of upstream dam increases, the hydrodynamic pressure on the dam is reduced. Moreover, when the Timoshenko beam theory is used, the system response increases. 展开更多
关键词 dam-reservoir-foundation interaction inclined dam explicit method semi-implicit method reservoir bottomabsorption free surface waves
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Explicit Symplectic Methods for the Nonlinear Schrodinger Equation 被引量:2
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作者 Hua Guan Yandong Jiao +1 位作者 Ju Liu Yifa Tang 《Communications in Computational Physics》 SCIE 2009年第8期639-654,共16页
By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integ... By performing a particular spatial discretization to the nonlinear Schrodinger equation(NLSE),we obtain a non-integrable Hamiltonian system which can be decomposed into three integrable parts(L-L-N splitting).We integrate each part by calculating its phase flow,and develop explicit symplectic integrators of different orders for the original Hamiltonian by composing the phase flows.A 2nd-order reversible constructed symplectic scheme is employed to simulate solitons motion and invariants behavior of the NLSE.The simulation results are compared with a 3rd-order non-symplectic implicit Runge-Kutta method,and the convergence of the formal energy of this symplectic integrator is also verified.The numerical results indicate that the explicit symplectic scheme obtained via L-L-N splitting is an effective numerical tool for solving the NLSE. 展开更多
关键词 explicit symplectic method L-L-N splitting nonlinear Schrodinger equation
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Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves 被引量:1
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作者 李山有 朱海燕 高淑芳 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2007年第2期191-196,共6页
In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complic... In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy. 展开更多
关键词 layered half-space wave scattering obliquely incidence artificial botmdary explicit finite element method Snell law
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A Study of Two Dimensional Unsteady MHD Free Convection Flow over a Vertical Plate 被引量:1
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作者 Absana Tarammim Mohammad Sharif Ullah Mohammed Jahir Uddin 《Open Journal of Fluid Dynamics》 2020年第4期342-355,共14页
In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum alo... In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum along energy are analyzed with suitable transformations. For numerical calculation, an implicit finite difference method is applied to solve a set of nonlinear dimensionless partial differential equations. Dimensionless velocity and temperature profile are also investigated due to the effects of assumed parameters in the concerned problem. An explicit finite difference technique is used to compute velocity and temperature profiles. The stability conditions are also examined. 展开更多
关键词 Free Convection Heat Transfer Flow Magnetic Field explicit Finite Difference Method
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Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates
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作者 LU JianFang SHU Chi-Wang ZHANG MengPing 《Science China Mathematics》 SCIE 2013年第12期2645-2676,共32页
In this paper,we analyze the explicit Runge-Kutta discontinuous Galerkin(RKDG)methods for the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology.The RKDG... In this paper,we analyze the explicit Runge-Kutta discontinuous Galerkin(RKDG)methods for the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology.The RKDG methods use a third order explicit total-variation-diminishing Runge-Kutta(TVDRK3)time discretization and upwinding numerical fluxes.By using the energy method,under a standard CourantFriedrichs-Lewy(CFL)condition,we obtain L2stability for general solutions and a priori error estimates when the solutions are smooth enough.The theoretical results are proved for piecewise polynomials with any degree k 1.Finally,since the solutions to this system are non-negative,we discuss a positivity-preserving limiter to preserve positivity without compromising accuracy.Numerical results are provided to demonstrate these RKDG methods. 展开更多
关键词 discontinuous Galerkin method explicit Runge-Kutta method stability error estimates corre-lated random walk positivity-preserving
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Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation
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作者 Yaming Chen Songhe Song Huajun Zhu 《Advances in Applied Mathematics and Mechanics》 SCIE 2014年第4期494-514,共21页
In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic sy... In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system.Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem,respectively.And the nonlinear subsystem is solved by a symplectic scheme.Finally,a composition method is applied to obtain the final schemes for the NLD equation.We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly.Numerical experiments are presented to show the effectiveness of the proposed methods. 展开更多
关键词 Nonlinear Dirac equation multi-symplectic method splitting method explicit method
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Damage tolerance of fractured rails on continuous welded rail track for high-speed railways
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作者 Yuan Gao Ping Wang +2 位作者 Kai Wang Jingmang Xu Zhiguo Dong 《Railway Engineering Science》 2021年第1期59-73,共15页
Broken gap is an extremely dangerous state in the service of high-speed rails,and the violent wheel–rail impact forces will be intensified when a vehicle passes the gap at high speeds,which may cause a secondary frac... Broken gap is an extremely dangerous state in the service of high-speed rails,and the violent wheel–rail impact forces will be intensified when a vehicle passes the gap at high speeds,which may cause a secondary fracture to rail and threaten the running safety of the vehicle.To recognize the damage tolerance of rail fracture length,the implicit–explicit sequential approach is adopted to simulate the wheel–rail high-frequency impact,which considers the factors such as the coupling effect between frictional contact and structural vibration,nonlinear material and real geometric profile.The results demonstrate that the plastic deformation and stress are distributed in crescent shape during the impact at the back rail end,increasing with the rail fracture length.The axle box acceleration in the frequency domain displays two characteristic modes with frequencies around 1,637 and 404 Hz.The limit of the rail fracture length is 60 mm for high-speed railway at a speed of 250 km/h. 展开更多
关键词 Rail broken gap explicit FE method DAMAGE High-frequency impact Stress mechanism
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Explicit High Order One-Step Methods for Decoupled Forward Backward Stochastic Differential Equations
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作者 Quan Zhou Yabing Sun 《Advances in Applied Mathematics and Mechanics》 SCIE 2021年第6期1293-1317,共25页
By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic d... By using the Feynman-Kac formula and combining with Itˆo-Taylor expansion and finite difference approximation,we first develop an explicit third order onestep method for solving decoupled forward backward stochastic differential equations.Then based on the third order one,an explicit fourth order method is further proposed.Several numerical tests are also presented to illustrate the stability and high order accuracy of the proposed methods. 展开更多
关键词 Decoupled forward backward stochastic differential equations Itˆo-Taylor expansion finite difference approximation explicit one-step method high order convergence
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A General Fractional Pollution Model for Lakes
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作者 Babak Shiri Dumitru Baleanu 《Communications on Applied Mathematics and Computation》 2022年第3期1105-1130,共26页
A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential e... A model for the amount of pollution in lakes connected with some rivers is introduced.In this model,it is supposed the density of pollution in a lake has memory.The model leads to a system of fractional differential equations.This system is transformed into a system of Volterra integral equations with memory kernels.The existence and regularity of the solutions are investigated.A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution.Validation examples are supported,and some models are simulated and discussed. 展开更多
关键词 Amount of pollution in lakes System of ordinary differential equations System of fractional differential equations explicit and implicit methods Regularity of the solution
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