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A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components 认领 引用 被引量：1
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作者 钱旭 宋松和 李伟斌 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第6期703-709,共7页
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ... Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis. 展开更多
关键词 conservative algorithm coupled nonlinear SchrSdinger equation multiply components unstablewave
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Data-Driven Algorithms for Finite-Horizon and Infinite-Horizon Indefinite Linear Quadratic Stochastic Optimal Control Problems 认领 引用
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作者 Guangchen Wang Heng Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第6期1459-1469,共11页
This paper is devoted to devising data-driven algorithms for finite-horizon and infinite-horizon linear quadratic stochastic optimal control(LQSOC)problems.In our study,the diffusion terms of system dynamics are permi... This paper is devoted to devising data-driven algorithms for finite-horizon and infinite-horizon linear quadratic stochastic optimal control(LQSOC)problems.In our study,the diffusion terms of system dynamics are permitted to hinge upon both control and state variables,and the weighting matrices of cost functionals are allowed to be indefinite.It is acknowledged that the optimal controls of finite-horizon and infinite-horizon indefinite LQSOC problems are correlated with a generalized differential Riccati equation(GDRE)and a generalized algebraic Riccati equation(GARE).Herein,we propose two data-driven algorithms to approximate the solutions of these Riccati equations,and thereby determine optimal controls,without leveraging the information of all system parameters.Additionally,we prove the convergence of these algorithms and examine the impact of computational errors.Finally,we validate the performance of these data-driven algorithms via three simulation examples. 展开更多
关键词 Data-driven algorithm generalized algebraic Riccati equation (GARE) generalized differential Riccati equation (GDRE) indefinite problem linear quadratic stochastic optimal control (LQSOC)
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A fast algorithm for solving the scattering problem from an open rectangular cavity 认领 引用
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作者 HAN Shangqi LI Yuan 《黑龙江大学自然科学学报》 CAS 2026年第1期31-41,共11页
This paper presents a fast algorithm for solving the scattering problem from an open rectangular cavity embedded in the ground plane.The computational region is chosen as the union of two rectangular regions:one is a ... This paper presents a fast algorithm for solving the scattering problem from an open rectangular cavity embedded in the ground plane.The computational region is chosen as the union of two rectangular regions:one is a region above the ground,the other one is a region containing the cavity.The finite difference scheme is constructed in each region.An intermediate layer of the mesh is shared by both regions,which is the key of the algorithm.A cyclic reduction method is employed to solve the difference equation in the region above the ground.Then the numerical solution on the cavity aperture can be obtained.The numerical experiments are provided to verify the feasibility of the proposed algorithm. 展开更多
关键词 scattering problem cavity Helmholtz equation fast algorithm difference equation cyclic reduction method
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A Gridless-Finite Volume Hybrid Algorithm for Euler Equations 认领 引用 被引量：5
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作者 马志华 陈红全 吴晓军 《Chinese Journal of Aeronautics》 EI CAS 2006年第4期286-294,共9页
A fast hybrid algorithm based on gridless method coupled with finite volume method （FVM） is developed for the solution to Euler equations. Compared with pure gridless method, the efficiency of the hybrid algorithm i... A fast hybrid algorithm based on gridless method coupled with finite volume method （FVM） is developed for the solution to Euler equations. Compared with pure gridless method, the efficiency of the hybrid algorithm is improved to the level of finite volume method for most parts of the flow filed arc covered with grid cells. Moreover, the hybrid method is flexible to deal with the configurations as clouds of points are used to cover the region adjacent to the bodies. Mirror satellites and mirror grid cells arc introduced to the interface to accomplish data communication between the different parts of the flow field. The Euler Equations arc spatially discretized with finite volume method and gridless method in mesh and clouds of points respectively, and an explicit four-stage Runge-Kutta scheme is utilized to reach the steady-state solution. Internal flows in channels and external flows over airfoils arc investigated with hybrid method, and the solutions arc comparad to those using pure finite volume method and pure gridless method. Numerical examples show that the hybrid algorithm captures the shock waves accurately, and it is as efficient as fmite volume method. 展开更多
关键词 fluid mechanicsl hybrid algorithm： gridless method finite volume method Euler equations
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CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION 认领 引用 被引量：3
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作者 李锡夔 武文华 《Acta Mechanica Sinica》 SCIE EI CAS 1999年第4期371-382,共12页
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
关键词 convection-diffusion equation characteristic Galerkin method finite element procedure precise integration implicit algorithm
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MESH FREE ADAPTIVE ALGORITHM FOR SOLVING EULER EQUATIONS ON STRUCTURED GRID POINTS 认领 引用 被引量：3
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作者 马志华 陈红全 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2005年第4期271-275,共5页
A complete mesh free adaptive algorithm （MFAA）, with solution adaptation and geometric adaptation, is developed to improve the resolution of flow features and to replace traditional global refinement techniques in s... A complete mesh free adaptive algorithm （MFAA）, with solution adaptation and geometric adaptation, is developed to improve the resolution of flow features and to replace traditional global refinement techniques in structured grids. Unnecessary redundant points and elements are avoided by using the mesh free local clouds refinement technology in shock influencing regions and regions near large curvature places on the boundary. Inviscid compressible flows over NACA0012 and RAE2822 airfoils are computed. Finally numerical results validate the accuracy of the above method. 展开更多
关键词 mesh free adaptive algorithm local refinement Euler equations
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Parallel finite element algorithm based on full domain partition for stationary Stokes equations 认领 引用 被引量：1
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作者 尚月强 何银年 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第5期643-650,共8页
Based on the full domain partition, a parallel finite element algorithm for the stationary Stokes equations is proposed and analyzed. In this algorithm, each subproblem is defined in the entire domain. Majority of the... Based on the full domain partition, a parallel finite element algorithm for the stationary Stokes equations is proposed and analyzed. In this algorithm, each subproblem is defined in the entire domain. Majority of the degrees of freedom are associated with the relevant subdomain. Therefore, it can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. This allows the algorithm to be implemented easily with low communication costs. Numerical results are given showing the high efficiency of the parallel algorithm. 展开更多
关键词 Stokes equations finite element parallel algorithm full domain partition
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A two-grid algorithm based on Newton iteration for the stream function form of the Navier-Stokes equations 认领 引用 被引量：1
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作者 SHAO Xin-ping HAN Dan-fu 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期368-378,共11页
In this paper,we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations.The algorithm is constructed by reducing the original system to one small,nonlinear s... In this paper,we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations.The algorithm is constructed by reducing the original system to one small,nonlinear system on the coarse mesh space and two similar linear systems(with same stiffness matrix but different right-hand side)on the fine mesh space.The convergence analysis and error estimation of the algorithm are given for the case of conforming elements.Furthermore,the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error.Finally,we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations. 展开更多
关键词 Two-grid algorithm Navier-Stokes equations Stream function form Reynolds number Newton iteration.
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Improved gradient iterative algorithms for solving Lyapunov matrix equations 认领 引用 被引量：1
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作者 顾传青 范伟薇 《Journal of Shanghai University(English Edition)》 2008年第5期395-399,共5页
In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared wi... In this paper, an improved gradient iterative （GI） algorithm for solving the Lyapunov matrix equations is studied. Convergence of the improved method for any initial value is proved with some conditions. Compared with the GI algorithm, the improved algorithm reduces computational cost and storage. Finally, the algorithm is tested with GI several numerical examples. 展开更多
关键词 gradient iterative （GI） algorithm improved gradient iteration （GI） algorithm Lyapunov matrix equations convergence factor
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ANALYSIS OF SIMPLE SHEAR ENDOCHRONIC EQUATIONSFOR FINITE PLASTIC DEFORMATION 认领 引用
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作者 江五贵 黄明挥 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第1期85-91,共7页
Jaumann rate, generalized Jaumann rate,Fu rate and Wu rate were incorporated into endochronic equations for finite plastic deformation to analyze simple shear finite deformation. The results show that an oscillatory s... Jaumann rate, generalized Jaumann rate,Fu rate and Wu rate were incorporated into endochronic equations for finite plastic deformation to analyze simple shear finite deformation. The results show that an oscillatory shear stress and normal stress response to a monotonically increasing shear strain occurs when Jaumann rate objective model is adopted for hypoelastic or endochronic materials. The oscillatory response is dependent on objective rate adopted,independent on elastoplastic models. Normal stress is unequal to zero during simple shear finite deformation. 展开更多
关键词 finite deformation endochronic equation simple shear oscillation objective rate
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TWO TYPES OF NEW ALGORITHMS FOR FINDING EXPLICIT ANALYTICAL SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS 认领 引用
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作者 张鸿庆 闫振亚 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第12期1423-1431,共9页
The idea of AC = BD was applied to solve the nonlinear differential equations. Suppose that Au = 0 is a given equation to he solved and Dv = 0 is an equation to be easily solved. If the transformation u = Cv is obtain... The idea of AC = BD was applied to solve the nonlinear differential equations. Suppose that Au = 0 is a given equation to he solved and Dv = 0 is an equation to be easily solved. If the transformation u = Cv is obtained so that v satisfies Dv = 0, then the solutions for Au = 0 can be found. In order to illustrate this approach, several examples about the transformation C are given. 展开更多
关键词 nonlinear differential equations transformation algorithm analytical solution
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A Novel Multi-Modal Neurosymbolic Reasoning Intelligent Algorithm for BLMP Equation 认领 引用 被引量：1
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作者 Hanwen Zhang Runfa Zhang Qirang Liu 《Chinese Physics Letters》 SCIE EI CAS CSCD 2025年第10期13-17,共5页
The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona... The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space. 展开更多
关键词 intelligent algorithm dimensional Boiti Leon Manna Pempinelli equation fluid dynamicsshallow water wavesplasma physicsand nonlinear evolution equation condensed matter physicsthe neurosymbolic reasoning characterizing complex nonlinear dynamic phenomena analytical methods
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An iterative algorithm for solving a class of matrix equations 认领 引用
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作者 Minghui WANG Yan FENG 《控制理论与应用（英文版）》 2009年第1期68-72,共5页
In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration s... In this paper, an iterative algorithm is presented to solve the Sylvester and Lyapunov matrix equations. By this iterative algorithm, for any initial matrix X1, a solution X＊ can be obtained within finite iteration steps in the absence of roundoff errors. Some examples illustrate that this algorithm is very efficient and better than that of [ 1 ] and [2]. 展开更多
关键词 Iterative algorithm Conjugate gradient method Lyapunov matrix equation Sylvester matrix equation
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INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS 认领 引用
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作者 侯延仁 R.M.M.Mattheij 《Acta Mathematica Scientia》 SCIE 2003年第2期219-238,共20页
Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, togeth... Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper. 展开更多
关键词 Navier-Stokes equations error estimation inertial algorithms
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AN IMPLICIT ALGORITHM OF THIN LAYER EQUATIONS IN VISCOUS,TRANSONIC,TWO-PHASE NOZZLE FLOW 认领 引用
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作者 何洪庆 侯晓 +1 位作者 蔡体敏 吴心平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第4期323-334,共12页
Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to so... Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped. 展开更多
关键词 thin layer equations two-phase viscous transonic nozzle flow,implicit algorithm
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A variational quantum algorithm for the Poisson equation based on the banded Toeplitz systems 认领 引用
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作者 Xiaoqi Liu Yuedi Qu +1 位作者 Ming Li Shu-Qian Shen 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第4期23-33,共11页
To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before... To solve the Poisson equation it is usually possible to discretize it into solving the corresponding linear system Ax=b.Variational quantum algorithms(VQAs)for the discretized Poisson equation have been studied before.We present a VQA based on the banded Toeplitz systems for solving the Poisson equation with respect to the structural features of matrix A.In detail,we decompose the matrices A and A2into a linear combination of the corresponding banded Toeplitz matrix and sparse matrices with only a few non-zero elements.For the one-dimensional Poisson equation with different boundary conditions and the d-dimensional Poisson equation with Dirichlet boundary conditions,the number of decomposition terms is less than that reported in[Phys.Rev.A 2023108,032418].Based on the decomposition of the matrix,we design quantum circuits that efficiently evaluate the cost function.Additionally,numerical simulation verifies the feasibility of the proposed algorithm.Finally,the VQAs for linear systems of equations and matrix-vector multiplications with the K-banded Toeplitz matrix TnKare given,where TnK∈Rn×nand K∈O(ploylogn). 展开更多
关键词 variational quantum algorithm Poisson equation quantum circuit
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SIMPLE WAVES OF THE TWO DIMENSIONAL COMPRESSIBLE FULL EULER EQUATIONS 认领 引用 被引量：2
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作者 陈宇 周忆 《Acta Mathematica Scientia》 SCIE CSCD 2015年第4期855-875,共21页
In this paper, we establish the existence of four families of simple wave solu- tion for two dimensional compressible full Euler system in the self-similar plane. For the 2 × 2 quasilinear non-reducible hyperboli... In this paper, we establish the existence of four families of simple wave solu- tion for two dimensional compressible full Euler system in the self-similar plane. For the 2 × 2 quasilinear non-reducible hyperbolic system, there not necessarily exists any simple wave solution. We prove the result that there are simple wave solutions for this 4× 4 non- reducible hyperbolic system, its simple wave flow is covered by four straight characteristics λ0 =λ1,λA2, λ3 and the solutions keep constants along these lines. We also investigate the existence of simple wave solution for the isentropic relativistic hydrodynamic system in the self-similar plane. 展开更多
关键词 simple waves Euler equations characteristic decomposition
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Quantum algorithms for matrix operations and linear systems of equations 认领 引用 被引量：3
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作者 Wentao Qi Alexandr I Zenchuk +1 位作者 Asutosh Kumar Junde Wu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2024年第3期100-112,共13页
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-ve... Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the‘sender-receiver’model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver’s density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations. 展开更多
关键词 matrix operation systems of linear equations ‘sender-receiver’quantum computation model quantum algorithm
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PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS 认领 引用
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作者 王国荣 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 1993年第1期1-10,共10页
This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obt... This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise. 展开更多
关键词 Parallel algorithm the minimum-norm least-squares solution inconsistent linear equations generalized inverse.
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Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems 认领 引用 被引量：1
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作者 Aijuan Song Guohua Wu +1 位作者 Witold Pedrycz Ling Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第1期75-89,共15页
Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,... Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance. 展开更多
关键词 Evolutionary algorithm(EA) nonlinear equations systems(ENSs) problem domain knowledge variable reduction strategy(VRS)
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