The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data...The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration （ADPI） method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for eoloical models.展开更多
A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to t...A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.展开更多
The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcom...The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.展开更多
This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using prec...This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.展开更多
The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary diffe...The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.展开更多
An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise in...An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the展开更多
General purpose graphic processing unit （GPU） calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has ...General purpose graphic processing unit （GPU） calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method （PIM） for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.展开更多
The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was...The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was discussed in this study.To efficiently and accurately compute the exponential of the dynamics state matrix and the matrix functions due to external loads,an adaptively filtered precise integration method was proposed,which inherits the high precision of the precise integrationmethod,improves the computational efficiency and saves the memory required.Moreover,the perturbation method was introduced to avoid repeated computations of matrix exponential and terms due to external loads.Based on the filtering and perturbation techniques,an adaptively filtered precise integration method considering perturbation for stochastic dynamics problems was developed.Two numerical experiments,including a model of phononic crystal and a bridge model considering random parameters,were performed to test the performance of the proposed method in terms of accuracy and efficiency.Numerical results show that the accuracy and efficiency of the proposed method are better than those of the existing precise integration method,the Newmark-βmethod and the Wilson-θmethod.展开更多
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matr...This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.展开更多
The Non-uniform rational B-spline （NURBS） enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this pap...The Non-uniform rational B-spline （NURBS） enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper. The scaled boundary finite element method is a semi-analytical technique, which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction. In this method, only the boundary is discretized in the finite element sense leading to a re- duction of the spatial dimension by one with no fundamental solution required. Neverthe- less, in case of the complex geometry, a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often un- avoidable in the conventional finite element approach, which leads to huge computational efforts and loss of accuracy. NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape. In the proposed methodology, the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions, while the straight part of the boundary is discretized by the conventional Lagrange shape functions. Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analy- sis and the solution is obtained using the modified precise integration method. The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion. Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method. The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.展开更多
Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of un...Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.展开更多
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implic...Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.展开更多
In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show...In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show that this model has a simple algorithm and high data utilization,avoids the negative influences caused by the correlation among the data acquired from the difference method and its accuracy is improved compared with the difference method.In addition,the strict weight of CPⅢprecise trigonometric leveling control network was also discussed in this paper.The results demonstrate that the ranging error of trigonometric leveling can be neglected when the vertical angle is less than 3 degrees.The accuracy of CPⅢprecise trigonometric leveling control network has not changed significantly before and after strict weight.展开更多
With a three-dimensional semiclassical ensemble method, we theoretically investigated the nonsequential double ionization of Ar driven by the spatially inhomogeneous few-cycle negatively chirped laser pulses. Our resu...With a three-dimensional semiclassical ensemble method, we theoretically investigated the nonsequential double ionization of Ar driven by the spatially inhomogeneous few-cycle negatively chirped laser pulses. Our results show that the recollision time window can be precisely controlled within an isolated time interval of several hundred attoseconds, which is useful for understanding the subcycle correlated electron dynamics. More interestingly, the correlated electron momentum distribution (CEMD) exhibits a strong dependence on laser intensity. That is, at lower laser intensity, CEMD is located in the first quadrant. As the laser intensity increases,CEMD shifts almost completely to the second and fourth quadrants, and then gradually to the third quadrant.The underlying physics governing the CEMD's dependence on laser intensity is explained.展开更多
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this te...We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.展开更多
The HY-2 satellite carrying a satellite-borne GPS receiver is the first Chinese radar altimeter satellite, whose radial orbit determination precision must reach the centimeter level. Now HY-2 is in the test phase so t...The HY-2 satellite carrying a satellite-borne GPS receiver is the first Chinese radar altimeter satellite, whose radial orbit determination precision must reach the centimeter level. Now HY-2 is in the test phase so that the observations are not openly released. In order to study the precise orbit determination precision and procedure for HY-2 based on the satellite- borne GPS technique, the satellite-borne GPS data are simulated in this paper. The HY-2 satellite-borne GPS antenna can receive at least seven GPS satellites each epoch, which can validate the GPS receiver and antenna design. What＇s more, the precise orbit determination processing flow is given and precise orbit determination experiments are conducted using the HY-2-borne GPS data with both the reduced-dynamic method and the kinematic geometry method. With the 1 and 3 mm phase data random errors, the radial orbit determination precision can achieve the centimeter level using these two methods and the kinematic orbit accuracy is slightly lower than that of the reduced-dynamic orbit. The earth gravity field model is an important factor which seriously affects the precise orbit determination of altimeter satellites. The reduced-dynamic orbit determination experiments are made with different earth gravity field models, such as EIGEN2, EGM96, TEG4, and GEMT3. Using a large number of high precision satellite-bome GPS data, the HY-2 precise orbit determination can reach the centimeter level with commonly used earth gravity field models up to above 50 degrees and orders.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
After the trajectory simulation model of rudder control rocket with six degrees of freedom is established by Matlab/ Simulink, the simulated targeting of rudder control rocket with rudder angle error and starting cont...After the trajectory simulation model of rudder control rocket with six degrees of freedom is established by Matlab/ Simulink, the simulated targeting of rudder control rocket with rudder angle error and starting control moment error is carried out respectively by means of Monte Carlo method and the distribution of impact points of rudder control rocket is counted from all the successful subsamples. In the case of adding interference errors associated with rudder angle error and starting time error, the simulation analysis of impact point dispersion is done and its lateral and longitudinal correction abilities at different targeting angles are simulated to identify the effects of these factors on characteristics and control precision of the rudder control rocket, which provides the relevant reference for high-precision design of rudder control system.展开更多
This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analys...This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analysis so that the parameter N, which has been takenas a constant and an independent pa- rameter without consideration ofthe problems in the original method, can be generated automaticallyby the algorithm itself.展开更多
基金supported by the National Science and Technology Major Project of China(Grant No. 2011ZX05004-003,2011ZX05014-006-006)the National Key Basic Research Program of China(Grant No. 2013CB228602)the Natural Science Foundation of China(Grant No. 40974066)
文摘The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration （ADPI） method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for eoloical models.
基金supported by the National Natural Science Foundation of China (Nos. 10902020 and 10721062)
文摘A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.
文摘The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.
文摘This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.
文摘The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.
基金Project supported by the National Natural Science Foundation of China(Nos.10902020 and 10721062)
文摘An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the
基金supported by the National Natural Science Foundation of China (Nos 40974066 and 40821062)National Basic Research Program of China (No 2007CB209602)
文摘General purpose graphic processing unit （GPU） calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method （PIM） for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.
基金the support of the National Natural Science Foundation of China(Grant Nos.11472067 and 51609034)the Science Foundation of Liaoning Province of China(No.2021-MS-119)+1 种基金the Dalian Youth Science and Technology Star Project(No.2018RQ06)the Fundamental Research Funds for the Central Universities(Grant No.DUT20GJ216).
文摘The difficulty in solving stochastic dynamics problems lies in the need for a large number of repeated computations of deterministic dynamic equations,which has been a challenge in stochastic dynamics analysis and was discussed in this study.To efficiently and accurately compute the exponential of the dynamics state matrix and the matrix functions due to external loads,an adaptively filtered precise integration method was proposed,which inherits the high precision of the precise integrationmethod,improves the computational efficiency and saves the memory required.Moreover,the perturbation method was introduced to avoid repeated computations of matrix exponential and terms due to external loads.Based on the filtering and perturbation techniques,an adaptively filtered precise integration method considering perturbation for stochastic dynamics problems was developed.Two numerical experiments,including a model of phononic crystal and a bridge model considering random parameters,were performed to test the performance of the proposed method in terms of accuracy and efficiency.Numerical results show that the accuracy and efficiency of the proposed method are better than those of the existing precise integration method,the Newmark-βmethod and the Wilson-θmethod.
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations（ODEs） are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
基金Project supported by the National Natural Science Foundation of China(No.10672194)the China-Russia Cooperative Project(the National Natural Science Foundation of China and the Russian Foundation for Basic Research)(No.10811120012)
文摘This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.
基金support by the National Natural Science Foundation of China(grant No.51779033,51409038)the National Key Research and Development Plan(grant No.2016YFB0201001)the National Natural Science Foundation of China(grant No.51421064)
文摘The Non-uniform rational B-spline （NURBS） enhanced scaled boundary finite element method in combination with the modified precise integration method is proposed for the transient heat conduction problems in this paper. The scaled boundary finite element method is a semi-analytical technique, which weakens the governing differential equations along the circumferential direction and solves those analytically in the radial direction. In this method, only the boundary is discretized in the finite element sense leading to a re- duction of the spatial dimension by one with no fundamental solution required. Neverthe- less, in case of the complex geometry, a huge number of elements are generally required to properly approximate the exact shape of the domain and distorted meshes are often un- avoidable in the conventional finite element approach, which leads to huge computational efforts and loss of accuracy. NURBS are the most popular mathematical tool in CAD industry due to its flexibility to fit any free-form shape. In the proposed methodology, the arbitrary curved boundary of problem domain is exactly represented with NURBS basis functions, while the straight part of the boundary is discretized by the conventional Lagrange shape functions. Both the concepts of isogeometric analysis and scaled boundary finite element method are combined to form the governing equations of transient heat conduction analy- sis and the solution is obtained using the modified precise integration method. The stiffness matrix is obtained from a standard quadratic eigenvalue problem and the mass matrix is determined from the low-frequency expansion. Finally the governing equations become a system of first-order ordinary differential equations and the time domain response is solved numerically by the modified precise integration method. The accuracy and stability of the proposed method to deal with the transient heat conduction problems are demonstrated by numerical examples.
基金supported by the National Natural Science Foundation of China(No.92252201)the Fundamental Research Funds for the Central Universitiesthe Academic Excellence Foundation of Beihang University(BUAA)for PhD Students。
文摘Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.
基金supported by ONR UMass Dartmouth Marine and UnderSea Technology(MUST)grant N00014-20-1-2849 under the project S31320000049160by DOE grant DE-SC0023164 sub-award RC114586-UMD+2 种基金by AFOSR grants FA9550-18-1-0383 and FA9550-23-1-0037supported by Michigan State University,by AFOSR grants FA9550-19-1-0281 and FA9550-18-1-0383by DOE grant DE-SC0023164.
文摘Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.
基金National Natural Science Foundation of China(No.41661091)。
文摘In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show that this model has a simple algorithm and high data utilization,avoids the negative influences caused by the correlation among the data acquired from the difference method and its accuracy is improved compared with the difference method.In addition,the strict weight of CPⅢprecise trigonometric leveling control network was also discussed in this paper.The results demonstrate that the ranging error of trigonometric leveling can be neglected when the vertical angle is less than 3 degrees.The accuracy of CPⅢprecise trigonometric leveling control network has not changed significantly before and after strict weight.
基金supported by the National Natural Science Foundation of China (Grant No. 12074329)Nanhu Scholars Program for Young Scholars of Xinyang Normal University。
文摘With a three-dimensional semiclassical ensemble method, we theoretically investigated the nonsequential double ionization of Ar driven by the spatially inhomogeneous few-cycle negatively chirped laser pulses. Our results show that the recollision time window can be precisely controlled within an isolated time interval of several hundred attoseconds, which is useful for understanding the subcycle correlated electron dynamics. More interestingly, the correlated electron momentum distribution (CEMD) exhibits a strong dependence on laser intensity. That is, at lower laser intensity, CEMD is located in the first quadrant. As the laser intensity increases,CEMD shifts almost completely to the second and fourth quadrants, and then gradually to the third quadrant.The underlying physics governing the CEMD's dependence on laser intensity is explained.
基金This research was supported by the National Natural Science Foundation of China （Nos. 41230210 and 41204074）, the Science Foundation of the Education Department of Yunnan Province （No. 2013Z152）, and Statoil Company （Contract No. 4502502663）.
文摘We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.
基金supported partially by the National Natural Science Foundation of China (Nos. 40974004 and 40974016)Key Laboratory of Dynamic Geodesy of CAS, China (No. L09-01) R&I Team Support Program and the Graduate Science and Technology Foundation of SDUST, China (No. YCA110403)
文摘The HY-2 satellite carrying a satellite-borne GPS receiver is the first Chinese radar altimeter satellite, whose radial orbit determination precision must reach the centimeter level. Now HY-2 is in the test phase so that the observations are not openly released. In order to study the precise orbit determination precision and procedure for HY-2 based on the satellite- borne GPS technique, the satellite-borne GPS data are simulated in this paper. The HY-2 satellite-borne GPS antenna can receive at least seven GPS satellites each epoch, which can validate the GPS receiver and antenna design. What＇s more, the precise orbit determination processing flow is given and precise orbit determination experiments are conducted using the HY-2-borne GPS data with both the reduced-dynamic method and the kinematic geometry method. With the 1 and 3 mm phase data random errors, the radial orbit determination precision can achieve the centimeter level using these two methods and the kinematic orbit accuracy is slightly lower than that of the reduced-dynamic orbit. The earth gravity field model is an important factor which seriously affects the precise orbit determination of altimeter satellites. The reduced-dynamic orbit determination experiments are made with different earth gravity field models, such as EIGEN2, EGM96, TEG4, and GEMT3. Using a large number of high precision satellite-bome GPS data, the HY-2 precise orbit determination can reach the centimeter level with commonly used earth gravity field models up to above 50 degrees and orders.
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.
文摘After the trajectory simulation model of rudder control rocket with six degrees of freedom is established by Matlab/ Simulink, the simulated targeting of rudder control rocket with rudder angle error and starting control moment error is carried out respectively by means of Monte Carlo method and the distribution of impact points of rudder control rocket is counted from all the successful subsamples. In the case of adding interference errors associated with rudder angle error and starting time error, the simulation analysis of impact point dispersion is done and its lateral and longitudinal correction abilities at different targeting angles are simulated to identify the effects of these factors on characteristics and control precision of the rudder control rocket, which provides the relevant reference for high-precision design of rudder control system.
基金the National Natural Science Foundation of China (No.19872016,19872017)the National Key Basic Research Special Foundation (G1999032805)the Foundation for University Key Teachers by the Ministry of Education of China
文摘This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analysis so that the parameter N, which has been takenas a constant and an independent pa- rameter without consideration ofthe problems in the original method, can be generated automaticallyby the algorithm itself.
