A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order pro...A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.展开更多
Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refrac...Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.展开更多
This paper addresses the synchronization of follower agents’state vectors with that of a leader in high-order nonlinear multi-agent systems.The proposed low-complexity control scheme employs high-gain observers to es...This paper addresses the synchronization of follower agents’state vectors with that of a leader in high-order nonlinear multi-agent systems.The proposed low-complexity control scheme employs high-gain observers to estimate higher-order synchronization errors,enabling the controller to rely solely on relative output measurements.This approach significantly reduces the dependence on full-state information,which is often infeasible or costly in practical engineering applications.An output feedback control strategy is developed to overcome these limitations while ensuring robust and effective synchronization.Simulation results are provided to demonstrate the effectiveness of the proposed approach and validate the theoretical findings.展开更多
High-precision optical frequency measurement serves as a cornerstone of modern science and technology,enabling advancements in fields ranging from fundamental physics to quantum information technologies.Obtaining prec...High-precision optical frequency measurement serves as a cornerstone of modern science and technology,enabling advancements in fields ranging from fundamental physics to quantum information technologies.Obtaining precise photon frequencies,especially in the ultraviolet or even extreme ultraviolet regimes,is a key goal in both light–matter interaction experiments and engineering applications.High-order harmonic generation(HHG)is an ideal light source for producing such photons.In this work,we propose an optical temporal interference model(OTIM)that establishes an analogy with multi-slit Fraunhofer diffraction(MSFD)to manipulate fine-frequency photon generation by exploiting the temporal coherence of HHG processes.Our model provides a unified physical framework for three distinct non-integer HHG generation schemes:single-pulse,shaped-pulse,and laser pulse train approaches,which correspond to single-MSFD-like,double-MSFD-like,and multi-MSFD-like processes,respectively.Arbitrary non-integer HHG photons can be obtained using our scheme.Our approach provides a new perspective for accurately measuring and controlling photon frequencies in fields such as frequency comb technology,interferometry,and atomic clocks.展开更多
The high-order deformation effects in even-even^(246,248)No are investigated by means of pairing self-consistent WoodsSaxon-Strutinsky calculations using the potential-energy-surface(PES)approach in an extended deform...The high-order deformation effects in even-even^(246,248)No are investigated by means of pairing self-consistent WoodsSaxon-Strutinsky calculations using the potential-energy-surface(PES)approach in an extended deformation space(β_(2),β_(3),β_(4),β_(5),β_(6),β_(7),β_(8)).Based on the calculated two-dimensional projected energy maps and different potential energy curves,we found that the highly even-order deformations have an important impact on both the fission trajectory and energy minima,while the odd-order deformations,accompanying the even-order ones,primarily affect the fission path beyond the second barrier.Relative to the light actinide nuclei,the nuclear ground state changes to the superdeformed configuration,but the normally deformed minimum,as the low-energy shape isomer,may still be primarily responsible for enhancing nuclear stability and ensuring experimental accessibility in^(246,248)No.Our present investigation indicates the nonnegligible impact of high-order deformation effects along the fission valley and will be helpful for deepening the understanding of different deformation effects and deformation couplings in nuclei,especially in this neutron-deficient heavy-mass region.展开更多
This paper is dedicated to solving the problem of adaptive fuzzy fault-tolerant tracking control for a class of time-varying high-order uncertain nonlinear systems.The motivation comes from how to construct a compact ...This paper is dedicated to solving the problem of adaptive fuzzy fault-tolerant tracking control for a class of time-varying high-order uncertain nonlinear systems.The motivation comes from how to construct a compact set large enough in which the approximation of any unknown continuous function by a fuzzy logic system(FLS)is effective while compensating sensor/actuator faults and external disturbances.The difficulty is to verify the boundedness of closed-loop signals on the constructed compact set and to reduce the number of the variables of the fuzzy membership functions as many as possible.By a new lemma,linear/nonlinear terms are introduced in adaptive laws to dominate unknown residual terms.With adding a power integrator method,a unified fault-tolerant controller is designed to drive the tracking error to converge to a small compact set of the origin within a fixed time,regardless of whether the system suffers from faults and disturbances.Superior to the existing results,in the presence of time-varying factors the scheme of this paper clarifies the logical relationship between the compactness of the approximation and the boundedness of the state variables.Finally,the application of control strategy is demonstrated by numerical/practical examples.展开更多
A dynamic graph(DG)is adopted to portray the evolving interplay between nodes in real-world scenarios prevalently.A high-order graph convolutional network(HGCN)is equipped with the ability to represent a DG by the spa...A dynamic graph(DG)is adopted to portray the evolving interplay between nodes in real-world scenarios prevalently.A high-order graph convolutional network(HGCN)is equipped with the ability to represent a DG by the spatial-temporal message passing mechanism built on tensor product.Concretely,an HGCN utilizes the discrete Fourier transform(DFT)to implement temporal message passing and then employs face-wise product to realize spatial message passing.However,DFT is only a special case of assorted time-frequency transforms,which considers the complex temporal patterns partially,thereby resulting in an inaccurate temporal message passing possibly.To address this issue,this study proposes six advanced time-frequency transform-incorporated HGCNs(TF-HGCNs)with discrete Fourier,discrete Hartley,discrete cosine,Haar wavelet,Walsh Hadamard,and slant transforms.In addition,a potent ensemble is built regarding the proposed six TF-HGCNs as the bases.Finally,the corresponding theoretical proof is presented.Empirical studies on six DG datasets demonstrate that owing to diverse time-frequency transforms,the proposed six TF-HGCNs significantly outperform state-of-the-art models in addressing the task of link weight estimation.Moreover,their ensemble outstrips each base's performance.展开更多
In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled...In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.展开更多
This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference m...This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.展开更多
Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonline...Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonlinear scheme （WCNS）, and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the Y-Reo transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity pro- file in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.展开更多
The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the probl...The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square（LS） and Moving-Least-Square（MLS） methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.展开更多
An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. I...An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.展开更多
The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ...The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.展开更多
A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An...A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An NURBS surface is used to precisely represent the hull geometry. Velocity potential on the hull surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and infinite image method is used to deal with the finite water depth effect. The time stepping method is used to solve the velocity potential at each time step. Detailed convergence study with respect to time step, panel size and Green function is undertaken. The present results of hydrodynamic forces are compared with those obtained by slender-body theory to show the validity of the proposed numerical method. Calculations are conducted for different water depths and lateral distances between ships, and the detail results are presented to demonstrate the effects of these factors.展开更多
This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton）...This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.展开更多
This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been...This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.展开更多
A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a G...A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.展开更多
To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this meth...To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this method,only one set of high-order pseudo-random waveforms,which contains all target frequencies,is needed.Based on high-order sequence pseudo-random signal construction algorithm,the waveform can be customized according to different exploration tasks.And the receivers are independent with each other and dynamically adjust the acquisition parameters according to different requirements.A field test in the deep iron ore of Qihe−Yucheng showed that the distributed WFEM based on high-order pseudo-random signal realizes the high-efficiency acquisition of massive electromagnetic data in quite a short time.Compared with traditional controlled-source electromagnetic methods,the distributed WFEM is much more efficient.Distributed WFEM can be applied to the large scale and high-resolution exploration for deep resources and minerals.展开更多
This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept...This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.展开更多
Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic sca...Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic scattering problems. The numerical solutions of two examples are correct compared with Method Of Moment(MOM).展开更多
文摘A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.
文摘Models of the coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations. Many methods used to solve coupled nonlinear Schr<span style="white-space:nowrap;">ödinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.
文摘This paper addresses the synchronization of follower agents’state vectors with that of a leader in high-order nonlinear multi-agent systems.The proposed low-complexity control scheme employs high-gain observers to estimate higher-order synchronization errors,enabling the controller to rely solely on relative output measurements.This approach significantly reduces the dependence on full-state information,which is often infeasible or costly in practical engineering applications.An output feedback control strategy is developed to overcome these limitations while ensuring robust and effective synchronization.Simulation results are provided to demonstrate the effectiveness of the proposed approach and validate the theoretical findings.
基金supported by the National Natural Science Foundation of China(Grant No.12304379)the Natural Science Foundation of Liaoning Province(Grant No.2024BS-269)the Guangdong Basic and Applied Basic Research Foundation(Grant No.025A1515011117)。
文摘High-precision optical frequency measurement serves as a cornerstone of modern science and technology,enabling advancements in fields ranging from fundamental physics to quantum information technologies.Obtaining precise photon frequencies,especially in the ultraviolet or even extreme ultraviolet regimes,is a key goal in both light–matter interaction experiments and engineering applications.High-order harmonic generation(HHG)is an ideal light source for producing such photons.In this work,we propose an optical temporal interference model(OTIM)that establishes an analogy with multi-slit Fraunhofer diffraction(MSFD)to manipulate fine-frequency photon generation by exploiting the temporal coherence of HHG processes.Our model provides a unified physical framework for three distinct non-integer HHG generation schemes:single-pulse,shaped-pulse,and laser pulse train approaches,which correspond to single-MSFD-like,double-MSFD-like,and multi-MSFD-like processes,respectively.Arbitrary non-integer HHG photons can be obtained using our scheme.Our approach provides a new perspective for accurately measuring and controlling photon frequencies in fields such as frequency comb technology,interferometry,and atomic clocks.
基金supported by the Natural Science Foundation of Henan Province(No.252300421478)the National Natural Science Foundation of China(Nos.11975209,U2032211,12075287)。
文摘The high-order deformation effects in even-even^(246,248)No are investigated by means of pairing self-consistent WoodsSaxon-Strutinsky calculations using the potential-energy-surface(PES)approach in an extended deformation space(β_(2),β_(3),β_(4),β_(5),β_(6),β_(7),β_(8)).Based on the calculated two-dimensional projected energy maps and different potential energy curves,we found that the highly even-order deformations have an important impact on both the fission trajectory and energy minima,while the odd-order deformations,accompanying the even-order ones,primarily affect the fission path beyond the second barrier.Relative to the light actinide nuclei,the nuclear ground state changes to the superdeformed configuration,but the normally deformed minimum,as the low-energy shape isomer,may still be primarily responsible for enhancing nuclear stability and ensuring experimental accessibility in^(246,248)No.Our present investigation indicates the nonnegligible impact of high-order deformation effects along the fission valley and will be helpful for deepening the understanding of different deformation effects and deformation couplings in nuclei,especially in this neutron-deficient heavy-mass region.
基金supported by National Natural Science Foundation of China[grant number 62173208]Taishan Scholar Project of Shandong Province of China[grant number tsqn202103061]。
文摘This paper is dedicated to solving the problem of adaptive fuzzy fault-tolerant tracking control for a class of time-varying high-order uncertain nonlinear systems.The motivation comes from how to construct a compact set large enough in which the approximation of any unknown continuous function by a fuzzy logic system(FLS)is effective while compensating sensor/actuator faults and external disturbances.The difficulty is to verify the boundedness of closed-loop signals on the constructed compact set and to reduce the number of the variables of the fuzzy membership functions as many as possible.By a new lemma,linear/nonlinear terms are introduced in adaptive laws to dominate unknown residual terms.With adding a power integrator method,a unified fault-tolerant controller is designed to drive the tracking error to converge to a small compact set of the origin within a fixed time,regardless of whether the system suffers from faults and disturbances.Superior to the existing results,in the presence of time-varying factors the scheme of this paper clarifies the logical relationship between the compactness of the approximation and the boundedness of the state variables.Finally,the application of control strategy is demonstrated by numerical/practical examples.
基金supported in part by the National Natural Science Foundation of China(62372385,62272078,62002337)Chongqing Natural Science Foundation(CSTB2022NSCQ-MSX1486,CSTB2023NSCQ-LZX0069)。
文摘A dynamic graph(DG)is adopted to portray the evolving interplay between nodes in real-world scenarios prevalently.A high-order graph convolutional network(HGCN)is equipped with the ability to represent a DG by the spatial-temporal message passing mechanism built on tensor product.Concretely,an HGCN utilizes the discrete Fourier transform(DFT)to implement temporal message passing and then employs face-wise product to realize spatial message passing.However,DFT is only a special case of assorted time-frequency transforms,which considers the complex temporal patterns partially,thereby resulting in an inaccurate temporal message passing possibly.To address this issue,this study proposes six advanced time-frequency transform-incorporated HGCNs(TF-HGCNs)with discrete Fourier,discrete Hartley,discrete cosine,Haar wavelet,Walsh Hadamard,and slant transforms.In addition,a potent ensemble is built regarding the proposed six TF-HGCNs as the bases.Finally,the corresponding theoretical proof is presented.Empirical studies on six DG datasets demonstrate that owing to diverse time-frequency transforms,the proposed six TF-HGCNs significantly outperform state-of-the-art models in addressing the task of link weight estimation.Moreover,their ensemble outstrips each base's performance.
基金Supported by the National Natural Science Foundation of China(Grant No.12261017)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022ZCZX077)。
文摘In this work, an efficient spectral method is proposed to solve the fourth-order eigenvalue problem in cylinder domain. Firstly, the key point of this method is to decompose the original model into a kind of decoupled two-dimensional eigenvalue problem by cylindrical coordinate transformation and Fourier series expansion, and deduce the crucial essential pole conditions. Secondly, we define a kind of weighted Sobolev spaces, and establish a suitable variational formula and its discrete form for each two-dimensional eigenvalue problem. Furthermore, we derive the equivalent operator formulas and obtain some prior error estimates of spectral theory of compact operators. More importantly, we further obtained error estimates for approximating eigenvalues and eigenfunctions by using two newly constructed projection operators. Finally,some numerical experiments are performed to validate our theoretical results and algorithm.
文摘This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.
基金supported by the National Basic Research Program of China(No.2014CB744803)
文摘Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonlinear scheme （WCNS）, and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the Y-Reo transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity pro- file in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.
基金funding from the European Community’s Seventh Framework Program (FP7/2007-2013) under grant agreement 225967 ‘‘Next Mu SE”supported by the National Natural Science Foundation of China (Nos. 11202013, 11572025 and 51420105008)
文摘The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square（LS） and Moving-Least-Square（MLS） methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.
基金co-supported by the National High Technology Research and Development Program of China(No.2015AA015303)the National Natural Science Foundation of China(No.11272152)+1 种基金the Aeronautical Science Foundation of China(No.20152752033)the Open Project of Key Laboratory of Aerodynamic Noise Control
文摘An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.
文摘The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.
基金the National Natural Science Foundation of China(Nos.51179019 and 51309152)
文摘A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An NURBS surface is used to precisely represent the hull geometry. Velocity potential on the hull surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and infinite image method is used to deal with the finite water depth effect. The time stepping method is used to solve the velocity potential at each time step. Detailed convergence study with respect to time step, panel size and Green function is undertaken. The present results of hydrodynamic forces are compared with those obtained by slender-body theory to show the validity of the proposed numerical method. Calculations are conducted for different water depths and lateral distances between ships, and the detail results are presented to demonstrate the effects of these factors.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10871117 and 10571110)
文摘This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.
基金supported by an Early Career Faculty grant from NASA's Space Technology Research Grants Programprovided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center
文摘This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.
基金supported by the National Natural Science Foundation of China(Nos.11502103 and11421062)the Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ15115)
文摘A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.
基金funded by the National Natural Science Foundation of China(No.42004056)the Natural Science Foundation of Shangdong Province,China(No.ZR2020QD052)China Postdoctoral Science Foundation(No.2019M652386)。
文摘To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this method,only one set of high-order pseudo-random waveforms,which contains all target frequencies,is needed.Based on high-order sequence pseudo-random signal construction algorithm,the waveform can be customized according to different exploration tasks.And the receivers are independent with each other and dynamically adjust the acquisition parameters according to different requirements.A field test in the deep iron ore of Qihe−Yucheng showed that the distributed WFEM based on high-order pseudo-random signal realizes the high-efficiency acquisition of massive electromagnetic data in quite a short time.Compared with traditional controlled-source electromagnetic methods,the distributed WFEM is much more efficient.Distributed WFEM can be applied to the large scale and high-resolution exploration for deep resources and minerals.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50508012)
文摘This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.
基金Supported by the National Natural Science Fbundation of China(No.60371003)
文摘Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic scattering problems. The numerical solutions of two examples are correct compared with Method Of Moment(MOM).
