Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the...Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the structural dynamics in multi-scale both the space domain and time domain.The discrete FEA model is partitioned into explicit and implicit parts using the nodal partition method.Multiple boundary node method is adopted to handle the interface coupled problem.In coupled region,the implicit Newmark coupled with an explicit predictor corrector Newmark whose predictive wave propagates into the implicit mesh.During the explicit subcycling process,the variables of boundary nodes are solved directly by dynamics equilibrium equation.The dissipation energy is dynamically determined in accordance with the energy balance checking.A cantilever beam and a building two numerical examples are proposed to verify that the method can greatly reduce the computing time while maintaining a high accuracy.展开更多
This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration sch...This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.展开更多
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearitie...The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.展开更多
To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of...To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.展开更多
With the booming development of terrestrial network, scaling terrestrial network over satellite network to build Integrated Terrestrial-Satellite Network(ITSN) and meanwhile to provide the global Internet access, has ...With the booming development of terrestrial network, scaling terrestrial network over satellite network to build Integrated Terrestrial-Satellite Network(ITSN) and meanwhile to provide the global Internet access, has become ever more attractive. Naturally, the widely and successfully used terrestrial routing protocols are the promising protocols to integrate the terrestrial and satellite networks. However, the terrestrial routing protocols, which rely on propagating routing messages to discover New Network Topology(NNT) in the terrestrial network with rare topology changes, will suffer from overly numerous routing messages in satellite network whose topology frequently changes as satellites move. In this paper, a Topology Discovery Sub-layer for ITSN Routing Schemes(TDS-IRS) is firstly proposed to avoid the propagation of numerous routing messages by taking advantage of the movement predictability of satellite and the requirements of routing schemes to discover NNT in advance of topology change. Secondly, a Weighted Perfect Matching based Topology Discovery(WPM-TD) model is designed to conduct the NNT discovery on the ground. Thirdly, this paper builds a testbed with real network devices and meanwhile interconnect that testbed with real Internet, to validate that RS-TDS can discover NNT immediately with the less on-board overhead compared with optimized routing schemes. Finally, different network scenarios are applied to validate the WPM-TD, i.e., the core module of TDS-IRS. Extensive experiments show WPM-TD can work efficiently, avoiding the invalid NNT discovery and decreasing 20% ~ 57% of potential topology changes, which can also improve up to 47% ~ 105% of network throughput.展开更多
By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antino...By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.展开更多
A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,...A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,and dispersion characteristics are achieved using appropriate values of the parameter.The proposed scheme has second-order accuracy with and without physical damping.Moreover,its stability,accuracy,and dispersion are analyzed.In addition,its performance is demonstrated by the two-dimensional scalar wave problem,the single-degree-of-freedom problem,two degrees-of-freedom spring system,and beam with boundary constraints.The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme.When the proposed scheme is applied to solve the wave problem,more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter.For the single-degree-offreedom system,two degrees-of-freedom system,and the time responses of beam,the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.展开更多
Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools wit...Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools within the framework of MD propagation,further development for better performance is still possible.The alternative version of LF in the middle thermostat scheme(LFmiddle)achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds.In this work,we perform a benchmark test of the two integrators(LF and LF-middle)in extensive conventional and enhanced sampling simulations,aiming at quantifying the time-stepsizeinduced variations of global properties(e.g.,detailed potential energy terms)as well as of local observables(e.g.,free energy changes or bondlengths)in practical simulations of complex systems.The test set is composed of six chemically and biologically relevant systems,including the conformational change of dihedral flipping in the N-methylacetamide and an AT(AdenineThymine)tract,the intra-molecular proton transfer inside malonaldehyde,the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A,the hydroxyl bond variations in ethaline deep eutectic solvent,and the potential energy of the blue-light using flavin photoreceptor.It is observed that the time-step-induced error is smaller for the LFmiddle scheme.The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables.Overall,the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.展开更多
In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.展开更多
This paper presents a ZUC-256 stream cipher algorithm hardware system in order to prevent the advanced security threats for 5 G wireless network.The main innovation of the hardware system is that a six-stage pipeline ...This paper presents a ZUC-256 stream cipher algorithm hardware system in order to prevent the advanced security threats for 5 G wireless network.The main innovation of the hardware system is that a six-stage pipeline scheme comprised of initialization and work stage is employed to enhance the solving speed of the critical logical paths.Moreover,the pipeline scheme adopts a novel optimized hardware structure to fast complete the Mod(231-1)calculation.The function of the hardware system has been validated experimentally in detail.The hardware system shows great superiorities.Compared with the same type system in recent literatures,the logic delay reduces by 47%with an additional hardware resources of only 4 multiplexers,the throughput rate reaches 5.26 Gbps and yields at least 45%better performance,the throughput rate per unit area increases 14.8%.The hardware system provides a faster and safer encryption module for the 5G wireless network.展开更多
The quantitative rules of the transfer and variation of errors,when the Gaussian integral functions F.(z) are evaluated sequentially by recurring,have been expounded.The traditional viewpoint to negate the applicabili...The quantitative rules of the transfer and variation of errors,when the Gaussian integral functions F.(z) are evaluated sequentially by recurring,have been expounded.The traditional viewpoint to negate the applicability and reliability of upward recursive formula in principle is amended.An optimal scheme of upward-and downward-joint recursions has been developed for the sequential F(z) computations.No additional accuracy is needed with the fundamental term of recursion because the absolute error of Fn(z) always decreases with the recursive approach.The scheme can be employed in modifying any of existent subprograms for Fn<z> computations.In the case of p-d-f-and g-type Gaussians,combining this method with Schaad's formulas can reduce,at least,the additive operations by a factor 40%;the multiplicative and exponential operations by a factor 60%.展开更多
The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is us...The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step size is chosen based on the size of the background cells.In May and Berger(J Sci Comput 71:919–943,2017),the mixed explicit-implicit approach in general and MUSCL-Trap(monotonic upwind scheme for conservation laws and trapezoidal scheme)in particular have been introduced to solve this problem by using implicit time stepping on the cut cells.Theoretical and numerical results have indicated that this might lead to a loss in accuracy when switching between the explicit and implicit time stepping.In this contribution,we examine this in more detail and will prove in one dimension that the specific combination MUSCL-Trap of an explicit second-order and an implicit second-order scheme results in a fully second-order mixed scheme.As this result is unlikely to hold in two dimensions,we also introduce two new versions of mixed explicit-implicit schemes based on exchanging the explicit scheme.We present numerical tests in two dimensions where we compare the new versions with the original MUSCL-Trap scheme.展开更多
This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twost...This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.展开更多
We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries （KdV） equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Za...We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries （KdV） equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.展开更多
基金supported by the National Key Research and Development Program of China(2016YFB0201800)the National Natural Science Foundation of China(No.51475287 and No.11772192).
文摘Many engineering applications need to analyse the system dynamics on the macro and micro level,which results in a larger computational effort.An explicit-implicit asynchronous step algorithm is introduced to solve the structural dynamics in multi-scale both the space domain and time domain.The discrete FEA model is partitioned into explicit and implicit parts using the nodal partition method.Multiple boundary node method is adopted to handle the interface coupled problem.In coupled region,the implicit Newmark coupled with an explicit predictor corrector Newmark whose predictive wave propagates into the implicit mesh.During the explicit subcycling process,the variables of boundary nodes are solved directly by dynamics equilibrium equation.The dissipation energy is dynamically determined in accordance with the energy balance checking.A cantilever beam and a building two numerical examples are proposed to verify that the method can greatly reduce the computing time while maintaining a high accuracy.
基金supported by National Natural Science Foundation of China under Grant No.10672143the Natural Science Foundation of Henan Province under Grant No.0511022200
文摘This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.
基金partially supported by the National Natural Science Foundation of China(Grant No.12071073)financial support by the Jiangsu Provincial Scientific Research Center of Applied Mathematics(Grant No.BK20233002).
文摘The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise,which possesses both Burgers-type and cubic nonlinearities.To discretize the continuous problem in space,we utilize a spectral Galerkin method.Subsequently,we introduce a nonlinear-tamed exponential integrator scheme,resulting in a fully discrete scheme.Within the framework of semigroup theory,this study provides precise estimations of the Sobolev regularity,L^(∞) regularity in space,and Hölder continuity in time for the mild solution,as well as for its semi-discrete and full-discrete approximations.Building upon these results,we establish moment boundedness for the numerical solution and obtain strong convergence rates in both spatial and temporal dimensions.A numerical example is presented to validate the theoretical findings.
基金The project supported by the National Key Program for Developing Basic Sciences (G1999043408 and G1998040901-1)the National Natural Sciences Foundation of China (40175024 and 40035010)
文摘To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.
基金supported by State Key Program of National Natural Science of China (91738202)Science &Technology Program of Beijing (Z171100005217001)
文摘With the booming development of terrestrial network, scaling terrestrial network over satellite network to build Integrated Terrestrial-Satellite Network(ITSN) and meanwhile to provide the global Internet access, has become ever more attractive. Naturally, the widely and successfully used terrestrial routing protocols are the promising protocols to integrate the terrestrial and satellite networks. However, the terrestrial routing protocols, which rely on propagating routing messages to discover New Network Topology(NNT) in the terrestrial network with rare topology changes, will suffer from overly numerous routing messages in satellite network whose topology frequently changes as satellites move. In this paper, a Topology Discovery Sub-layer for ITSN Routing Schemes(TDS-IRS) is firstly proposed to avoid the propagation of numerous routing messages by taking advantage of the movement predictability of satellite and the requirements of routing schemes to discover NNT in advance of topology change. Secondly, a Weighted Perfect Matching based Topology Discovery(WPM-TD) model is designed to conduct the NNT discovery on the ground. Thirdly, this paper builds a testbed with real network devices and meanwhile interconnect that testbed with real Internet, to validate that RS-TDS can discover NNT immediately with the less on-board overhead compared with optimized routing schemes. Finally, different network scenarios are applied to validate the WPM-TD, i.e., the core module of TDS-IRS. Extensive experiments show WPM-TD can work efficiently, avoiding the invalid NNT discovery and decreasing 20% ~ 57% of potential topology changes, which can also improve up to 47% ~ 105% of network throughput.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
文摘A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics.The proposed method is a oneparameter non-dissipative scheme.Improved stability,accuracy,and dispersion characteristics are achieved using appropriate values of the parameter.The proposed scheme has second-order accuracy with and without physical damping.Moreover,its stability,accuracy,and dispersion are analyzed.In addition,its performance is demonstrated by the two-dimensional scalar wave problem,the single-degree-of-freedom problem,two degrees-of-freedom spring system,and beam with boundary constraints.The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme.When the proposed scheme is applied to solve the wave problem,more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter.For the single-degree-offreedom system,two degrees-of-freedom system,and the time responses of beam,the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.
基金supported by the National Natural Science Foundation of China(No.21961142017)the Ministry of Science and Technology of China(No.2017YFA0204901)。
文摘Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools within the framework of MD propagation,further development for better performance is still possible.The alternative version of LF in the middle thermostat scheme(LFmiddle)achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds.In this work,we perform a benchmark test of the two integrators(LF and LF-middle)in extensive conventional and enhanced sampling simulations,aiming at quantifying the time-stepsizeinduced variations of global properties(e.g.,detailed potential energy terms)as well as of local observables(e.g.,free energy changes or bondlengths)in practical simulations of complex systems.The test set is composed of six chemically and biologically relevant systems,including the conformational change of dihedral flipping in the N-methylacetamide and an AT(AdenineThymine)tract,the intra-molecular proton transfer inside malonaldehyde,the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A,the hydroxyl bond variations in ethaline deep eutectic solvent,and the potential energy of the blue-light using flavin photoreceptor.It is observed that the time-step-induced error is smaller for the LFmiddle scheme.The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables.Overall,the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.
基金supported in part by the National R&D Program for Major Research Instruments of China(Grant No:62027814)the National Natural Science Foundation of China(Grant No:62104054)+2 种基金the Natural Science Foundation of Heilongjiang Province(Grant No:F2018010)the Postdoctoral Science Foundation of Heilongjiang Province,China(No:LBH-Z20133)the Fundamental Research Funds for The Central Universities,China(3072021CF0806)。
文摘This paper presents a ZUC-256 stream cipher algorithm hardware system in order to prevent the advanced security threats for 5 G wireless network.The main innovation of the hardware system is that a six-stage pipeline scheme comprised of initialization and work stage is employed to enhance the solving speed of the critical logical paths.Moreover,the pipeline scheme adopts a novel optimized hardware structure to fast complete the Mod(231-1)calculation.The function of the hardware system has been validated experimentally in detail.The hardware system shows great superiorities.Compared with the same type system in recent literatures,the logic delay reduces by 47%with an additional hardware resources of only 4 multiplexers,the throughput rate reaches 5.26 Gbps and yields at least 45%better performance,the throughput rate per unit area increases 14.8%.The hardware system provides a faster and safer encryption module for the 5G wireless network.
文摘The quantitative rules of the transfer and variation of errors,when the Gaussian integral functions F.(z) are evaluated sequentially by recurring,have been expounded.The traditional viewpoint to negate the applicability and reliability of upward recursive formula in principle is amended.An optimal scheme of upward-and downward-joint recursions has been developed for the sequential F(z) computations.No additional accuracy is needed with the fundamental term of recursion because the absolute error of Fn(z) always decreases with the recursive approach.The scheme can be employed in modifying any of existent subprograms for Fn<z> computations.In the case of p-d-f-and g-type Gaussians,combining this method with Schaad's formulas can reduce,at least,the additive operations by a factor 40%;the multiplicative and exponential operations by a factor 60%.
文摘The solution of time-dependent hyperbolic conservation laws on cut cell meshes causes the small cell problem:standard schemes are not stable on the arbitrarily small cut cells if an explicit time stepping scheme is used and the time step size is chosen based on the size of the background cells.In May and Berger(J Sci Comput 71:919–943,2017),the mixed explicit-implicit approach in general and MUSCL-Trap(monotonic upwind scheme for conservation laws and trapezoidal scheme)in particular have been introduced to solve this problem by using implicit time stepping on the cut cells.Theoretical and numerical results have indicated that this might lead to a loss in accuracy when switching between the explicit and implicit time stepping.In this contribution,we examine this in more detail and will prove in one dimension that the specific combination MUSCL-Trap of an explicit second-order and an implicit second-order scheme results in a fully second-order mixed scheme.As this result is unlikely to hold in two dimensions,we also introduce two new versions of mixed explicit-implicit schemes based on exchanging the explicit scheme.We present numerical tests in two dimensions where we compare the new versions with the original MUSCL-Trap scheme.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.
基金Supported by the National Baslc Research Programme under Grant No 2005CB321703, and the National Natural Science Foundation of China under Grant Nos 40221503, 10471067 and 40405019.
文摘We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries （KdV） equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration.
