This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent ...This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.展开更多
In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases a...In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases and investigated their finite sample properties. An empirical study is given to compare the performance of the proposed estimators with the existing estimators that utilize auxiliary variable(s) for finite population mean. It has been found that the generalized Ra-tio-cum-product estimator in full information case using multiple auxiliary variables is more efficient than mean per unit, ratio and product estimator using one auxiliary variable, ratio and product estimator using multiple auxiliary variable and ratio-cum-product estimators in both partial and no information case in two phase sampling. A generalized Ratio-cum-product estimator in partial information case is more efficient than Generalized Ratio-cum-product estimator in No information case.展开更多
In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important roles.The scalar auxiliary variable approach is int...In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important roles.The scalar auxiliary variable approach is introduced for the physical system;the mass conservation and energy dissipation is proved for the CHHS system.Subsequently,a fully discrete SAV finite element scheme is proposed,with the mass conservation and energy dissipation laws established at a theoretical level.In addition,the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.展开更多
In this paper,we present a quadratic auxiliary variable(QAV)technique to develop a novel class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation.The QAV approach is first utilized to...In this paper,we present a quadratic auxiliary variable(QAV)technique to develop a novel class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation.The QAV approach is first utilized to transform the original equation into a reformulated QAV system with a consistent initial condition.Then the reformulated QAV system is discretized by applying the Fourier pseudo-spectral method in space and the symplectic Runge-Kutta methods in time,which arrives at a class of fully discrete schemes.Under the consistent initial condition,they can be rewritten as a new fully discrete system by eliminating the introduced auxiliary variable,which is rigorously proved to be energy-preserving and symmetric.Ample numerical experiments are conducted to confirm the expected order of accuracy,conservative property and efficiency of the proposed methods.The presented numerical strategy makes it possible to directly apply a special class of Runge-Kutta methods to develop energy-preserving algorithms for a general conservative system with any polynomial energy.展开更多
A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical schem...A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical scheme linear while preserving the nonlinear energy stability,we make use of the scalar auxiliary variable(SAV)approach,in which a modified Crank-Nicolson is applied for the surface diffusion part.The energy stability could be derived a modified form,in comparison with the standard Crank-Nicolson approximation to the surface diffusion term.Such an energy stability leads to an H2 bound for the numerical solution.In addition,this H2 bound is not sufficient for the optimal rate convergence analysis,and we establish a uniform-in-time H3 bound for the numerical solution,based on the higher order Sobolev norm estimate,combined with repeated applications of discrete H¨older inequality and nonlinear embeddings in the Fourier pseudo-spectral space.This discrete H3 bound for the numerical solution enables us to derive the optimal rate error estimate for this alternate SAV method.A few numerical experiments are also presented,which confirm the efficiency and accuracy of the proposed scheme.展开更多
In the present paper,we propose an efficient scrambled estimator of population mean of quantitative sensitive study variable,using general linear transformation of nonsensitive auxiliary variable.Efficiency comparison...In the present paper,we propose an efficient scrambled estimator of population mean of quantitative sensitive study variable,using general linear transformation of nonsensitive auxiliary variable.Efficiency comparisons with the existing estimators have been carried out both theoretically and numerically.It has been found that our optimal scrambled estimator is always more efficient than most of the existing scrambled estimators and also it is more efficient than few other scrambled estimators under some conditions.展开更多
In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the mul...In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the multiple desired signals is realized by the improved Capon method. At the same time,the sidelobe constraint is added to reduce the sidelobe level. To reduce the pointing errors of multiple desired signals, the array response phase of the desired signal is firstly optimized by using auxilary variables while keeping the response amplitude unchanged. The whole design is formulated as a convex optimization problem solved by the branch-and-bound algorithm. In addition,the beamformer weight vector is penalized with the modified reweighted l_(1)-norm to achieve sparsity. Theoretical analysis and simulation results show that the proposed algorithm has lower sidelobe level, higher SINR, and less pointing error than the stateof-the-art methods in the case of a single expected signal and multiple desired signals.展开更多
In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mea...In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.展开更多
In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-depe...In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.展开更多
Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a nov...Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase changemodel,which is the coupling of a heat transfer equation and a phase field equation.The unconditional energy stability and consistency error estimates are rigorously proved for the proposed schemes.A detailed implementation demonstrates that the proposed method requires only the solution of a system of linear elliptic equations at each time step,with an efficient scheme of sufficient accuracy to calculate the solution at the first step.It is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time steps.Adaptive time step size strategies can be applied to further benefit from this unconditional stability.Numerical experiments are presented to verify the theoretical claims and to illustrate the accuracy and effectiveness of our method.展开更多
Abstract.In this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear...Abstract.In this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic form.We use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time discretization.Both mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta method.Numerical examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.展开更多
Label distribution learning(LDL)is a new learning paradigm to deal with label ambiguity and many researches have achieved the prominent performances.Compared with traditional supervised learning scenarios,the annotati...Label distribution learning(LDL)is a new learning paradigm to deal with label ambiguity and many researches have achieved the prominent performances.Compared with traditional supervised learning scenarios,the annotation with label distribution is more expensive.Direct use of existing active learning(AL)approaches,which aim to reduce the annotation cost in traditional learning,may lead to the degradation of their performance.To deal with the problem of high annotation cost in LDL,we propose the active label distribution learning via kernel maximum mean discrepancy(ALDL-kMMD)method to tackle this crucial but rarely studied problem.ALDL-kMMD captures the structural information of both data and label,extracts the most representative instances from the unlabeled ones by incorporating the nonlinear model and marginal probability distribution matching.Besides,it is also able to markedly decrease the amount of queried unlabeled instances.Meanwhile,an effective solution is proposed for the original optimization problem of ALDL-kMMD by constructing auxiliary variables.The effectiveness of our method is validated with experiments on the real-world datasets.展开更多
In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure syste...In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.展开更多
The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Sc...The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Schrodinger equation.First,we reformulate the equation as an canonical Hamiltonian system,and obtain a new equivalent system via introducing a scalar variable.Then,we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space direction.After that,applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete version.As expected,the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step.Finally,numerical experiments are provided to demonstrate the efficiency and conservation of the scheme.展开更多
In this paper,the Peng-Robinson equation of state with dynamic boundary conditions is discussed,which considers the interactions with solid walls.At first,the model is introduced and the regularization method on the n...In this paper,the Peng-Robinson equation of state with dynamic boundary conditions is discussed,which considers the interactions with solid walls.At first,the model is introduced and the regularization method on the nonlinear term is adopted.Next,The scalar auxiliary variable(SAV)method in temporal and finite element method in spatial are used to handle the Peng-Robinson equation of state.Then,the energy dissipation law of the numerical method is obtained.Also,we acquire the convergence of the discrete SAV finite element method(FEM).Finally,a numerical example is provided to confirm the theoretical result.展开更多
In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave eq...In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave equation.The schemes are linear,conserve mass and unconditionally dissipate a pseudo energy.We prove rigorously second-order error estimates in both time and space for the phase field variable in discrete norms.We also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.展开更多
In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are establis...In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions.The key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting approach.Numerical examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.展开更多
This paper develops a new approach to domain estimation and proposes a new class of ratio estimators that is more efficient than the regression estimator and not depending on any optimality condition using the princip...This paper develops a new approach to domain estimation and proposes a new class of ratio estimators that is more efficient than the regression estimator and not depending on any optimality condition using the principle of calibration weightings.Some wellknown regression and ratio-type estimators are obtained and shown to be special members of the newclass of estimators.Results of analytical study showed that the new class of estimators is superior in both efficiency and biasedness to all related existing estimators under review.The relative performances of the new class of estimators with a corresponding global estimator were evaluated through a simulation study.Analysis and evaluation are presented.展开更多
In this paper,we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation.The quadratic auxiliary variable approach is first pr...In this paper,we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation.The quadratic auxiliary variable approach is first proposed to reformulate the original model into an equivalent system,which transforms the energy conservation law of the Korteweg-de Vries equation into two quadratic invariants of the reformulated system.Then the symplectic Runge-Kutta methods are directly employed for the reformulated model to arrive at a new kind of time semi-discrete schemes for the original problem.Under consistent initial conditions,the proposed methods are rigorously proved to maintain the original energy conservation law of the Korteweg-de Vries equation.In addition,the Fourier pseudo-spectral method is used for spatial discretization,resulting in fully discrete energy-preserving schemes.To implement the proposed methods effectively,we present a very efficient iterative technique,which not only greatly saves the calculation cost,but also achieves the purpose of practically preserving structure.Ample numerical results are addressed to confirm the expected order of accuracy,conservative property and efficiency of the proposed algorithms.展开更多
基金supported by the National Natural Science Foundation of China(12126318,12126302).
文摘This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.
文摘In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases and investigated their finite sample properties. An empirical study is given to compare the performance of the proposed estimators with the existing estimators that utilize auxiliary variable(s) for finite population mean. It has been found that the generalized Ra-tio-cum-product estimator in full information case using multiple auxiliary variables is more efficient than mean per unit, ratio and product estimator using one auxiliary variable, ratio and product estimator using multiple auxiliary variable and ratio-cum-product estimators in both partial and no information case in two phase sampling. A generalized Ratio-cum-product estimator in partial information case is more efficient than Generalized Ratio-cum-product estimator in No information case.
基金supported by NSFC(Grant No.11871441)supported by NSF(Grant No.DMS-2012669).
文摘In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important roles.The scalar auxiliary variable approach is introduced for the physical system;the mass conservation and energy dissipation is proved for the CHHS system.Subsequently,a fully discrete SAV finite element scheme is proposed,with the mass conservation and energy dissipation laws established at a theoretical level.In addition,the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.
基金Yuezheng Gong’s work is partially supported by the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202002)the Fundamental Research Funds for the Central Universities(Grant No.NS2022070)+7 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220131)the National Natural Science Foundation of China(Grants Nos.12271252 and 12071216)Qi Hong’s work is partially supported by the National Natural Science Foundation of China(Grants No.12201297)the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202001)Chunwu Wang’s work is partially supported by Science Challenge Project(Grant No.TZ2018002)National Science and Technology Major Project(J2019-II-0007-0027)Yushun Wang’s work is partially supported by the National Key Research and Development Program of China(Grant No.2018YFC1504205)the National Natural Science Foundation of China(Grants No.12171245).
文摘In this paper,we present a quadratic auxiliary variable(QAV)technique to develop a novel class of arbitrarily high-order energy-preserving algorithms for the Camassa-Holm equation.The QAV approach is first utilized to transform the original equation into a reformulated QAV system with a consistent initial condition.Then the reformulated QAV system is discretized by applying the Fourier pseudo-spectral method in space and the symplectic Runge-Kutta methods in time,which arrives at a class of fully discrete schemes.Under the consistent initial condition,they can be rewritten as a new fully discrete system by eliminating the introduced auxiliary variable,which is rigorously proved to be energy-preserving and symmetric.Ample numerical experiments are conducted to confirm the expected order of accuracy,conservative property and efficiency of the proposed methods.The presented numerical strategy makes it possible to directly apply a special class of Runge-Kutta methods to develop energy-preserving algorithms for a general conservative system with any polynomial energy.
文摘A second order accurate(in time)numerical scheme is analyzed for the slope-selection(SS)equation of the epitaxial thin film growth model,with Fourier pseudo-spectral discretization in space.To make the numerical scheme linear while preserving the nonlinear energy stability,we make use of the scalar auxiliary variable(SAV)approach,in which a modified Crank-Nicolson is applied for the surface diffusion part.The energy stability could be derived a modified form,in comparison with the standard Crank-Nicolson approximation to the surface diffusion term.Such an energy stability leads to an H2 bound for the numerical solution.In addition,this H2 bound is not sufficient for the optimal rate convergence analysis,and we establish a uniform-in-time H3 bound for the numerical solution,based on the higher order Sobolev norm estimate,combined with repeated applications of discrete H¨older inequality and nonlinear embeddings in the Fourier pseudo-spectral space.This discrete H3 bound for the numerical solution enables us to derive the optimal rate error estimate for this alternate SAV method.A few numerical experiments are also presented,which confirm the efficiency and accuracy of the proposed scheme.
文摘In the present paper,we propose an efficient scrambled estimator of population mean of quantitative sensitive study variable,using general linear transformation of nonsensitive auxiliary variable.Efficiency comparisons with the existing estimators have been carried out both theoretically and numerically.It has been found that our optimal scrambled estimator is always more efficient than most of the existing scrambled estimators and also it is more efficient than few other scrambled estimators under some conditions.
基金the National Key Research and Development Program(2021YFB3502500).
文摘In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the multiple desired signals is realized by the improved Capon method. At the same time,the sidelobe constraint is added to reduce the sidelobe level. To reduce the pointing errors of multiple desired signals, the array response phase of the desired signal is firstly optimized by using auxilary variables while keeping the response amplitude unchanged. The whole design is formulated as a convex optimization problem solved by the branch-and-bound algorithm. In addition,the beamformer weight vector is penalized with the modified reweighted l_(1)-norm to achieve sparsity. Theoretical analysis and simulation results show that the proposed algorithm has lower sidelobe level, higher SINR, and less pointing error than the stateof-the-art methods in the case of a single expected signal and multiple desired signals.
文摘In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.
文摘In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.
文摘Thermal phase change problems are widespread in mathematics,nature,and science.They are particularly useful in simulating the phenomena of melting and solidification in materials science.In this paper we propose a novel class of arbitrarily high-order and unconditionally energy stable schemes for a thermal phase changemodel,which is the coupling of a heat transfer equation and a phase field equation.The unconditional energy stability and consistency error estimates are rigorously proved for the proposed schemes.A detailed implementation demonstrates that the proposed method requires only the solution of a system of linear elliptic equations at each time step,with an efficient scheme of sufficient accuracy to calculate the solution at the first step.It is observed from the comparison with the classical explicit Runge-Kutta method that the new schemes allow to use larger time steps.Adaptive time step size strategies can be applied to further benefit from this unconditional stability.Numerical experiments are presented to verify the theoretical claims and to illustrate the accuracy and effectiveness of our method.
基金Yi’s research was partially supported by NSFC Project(No.12071400)China’s National Key R&D Programs(No.2020YFA0713500)+2 种基金Hunan Provincial NSF Project Yi’s research was partially supported by NSFC Project(No.12071400)China’s National Key R&D Programs(No.2020YFA0713500)Hunan Provincial NSF Project。
文摘Abstract.In this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic form.We use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time discretization.Both mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta method.Numerical examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.
基金partially supported by the National Natural Science Fundation of China(Grant Nos.61922087,61906201 and 62006238)the Science and Technology Innovation Program of Hunan Province(2021RC3070).
文摘Label distribution learning(LDL)is a new learning paradigm to deal with label ambiguity and many researches have achieved the prominent performances.Compared with traditional supervised learning scenarios,the annotation with label distribution is more expensive.Direct use of existing active learning(AL)approaches,which aim to reduce the annotation cost in traditional learning,may lead to the degradation of their performance.To deal with the problem of high annotation cost in LDL,we propose the active label distribution learning via kernel maximum mean discrepancy(ALDL-kMMD)method to tackle this crucial but rarely studied problem.ALDL-kMMD captures the structural information of both data and label,extracts the most representative instances from the unlabeled ones by incorporating the nonlinear model and marginal probability distribution matching.Besides,it is also able to markedly decrease the amount of queried unlabeled instances.Meanwhile,an effective solution is proposed for the original optimization problem of ALDL-kMMD by constructing auxiliary variables.The effectiveness of our method is validated with experiments on the real-world datasets.
基金The first author would like to thank the support from the UM-Funded PhD Assistantship from University of MacaoThe second author was partially supported by Macao Young Scholar Program(AM201919)+5 种基金excellent youth project of Hunan Education Department(19B543)Hunan National Applied Mathematics Center of Hunan Provincial Science and Technology Department(2020ZYT003)The third author would like to thank financial support from National Natural Science Foundation of China(Grant Nos.11922120,11871489)FDCT of Macao SAR(Grant No.0082/2020/A2)University of Macao(Grant No.MYRG2020-00265-FST)Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications(Grant No.2020B1212030001).
文摘In this paper,based on the imaginary time gradient flow model in the density functional theory,a scalar auxiliary variable(SAV)method is developed for the ground state calculation of a given electronic structure system.To handle the orthonormality constraint on those wave functions,two kinds of penalty terms are introduced in designing the modified energy functional in SAV,i.e.,one for the norm preserving of each wave function,another for the orthogonality between each pair of different wave functions.A numerical method consisting of a designed scheme and a linear finite element method is used for the discretization.Theoretically,the desired unconditional decay of modified energy can be obtained from our method,while computationally,both the original energy and modified energy decay behaviors can be observed successfully from a number of numerical experiments.More importantly,numerical results show that the orthonormality among those wave functions can be automatically preserved,without explicitly preserving orthogonalization operations.This implies the potential of our method in large-scale simulations in density functional theory.
基金supported by the National Natural Science Foundation of China(Grant Nos.12171245,11971416,11971242)the Natural Science Foundation of Henan Province(No.222300420280)the Program for Scientific and Technological Innovation Talents in Universities of Henan Province(No.22HASTIT018).
文摘The main objective of this paper is to present an efficient structure-preserving scheme,which is based on the idea of the scalar auxiliary variable approach,for solving the twodimensional space-fractional nonlinear Schrodinger equation.First,we reformulate the equation as an canonical Hamiltonian system,and obtain a new equivalent system via introducing a scalar variable.Then,we construct a semi-discrete energy-preserving scheme by using the Fourier pseudo-spectral method to discretize the equivalent system in space direction.After that,applying the Crank-Nicolson method on the temporal direction gives a linearly-implicit scheme in the fully-discrete version.As expected,the proposed scheme can preserve the energy exactly and more efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step.Finally,numerical experiments are provided to demonstrate the efficiency and conservation of the scheme.
基金the National Natural Science Foundation of China(No.11871441).
文摘In this paper,the Peng-Robinson equation of state with dynamic boundary conditions is discussed,which considers the interactions with solid walls.At first,the model is introduced and the regularization method on the nonlinear term is adopted.Next,The scalar auxiliary variable(SAV)method in temporal and finite element method in spatial are used to handle the Peng-Robinson equation of state.Then,the energy dissipation law of the numerical method is obtained.Also,we acquire the convergence of the discrete SAV finite element method(FEM).Finally,a numerical example is provided to confirm the theoretical result.
基金supported by National Natural Science Foundation of China(Grant Nos.11901489 and 11971407)supported by National Science Foundation of USA(Grant No.DMS-1720442)。
文摘In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave equation.The schemes are linear,conserve mass and unconditionally dissipate a pseudo energy.We prove rigorously second-order error estimates in both time and space for the phase field variable in discrete norms.We also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.
基金supported by National Natural Science Foundation of China (Grant Nos. 11771162,11771128,11871106,11871092 and 11926356)National Safety Administration Fund (Grant No. U1930402)。
文摘In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions.The key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting approach.Numerical examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.
文摘This paper develops a new approach to domain estimation and proposes a new class of ratio estimators that is more efficient than the regression estimator and not depending on any optimality condition using the principle of calibration weightings.Some wellknown regression and ratio-type estimators are obtained and shown to be special members of the newclass of estimators.Results of analytical study showed that the new class of estimators is superior in both efficiency and biasedness to all related existing estimators under review.The relative performances of the new class of estimators with a corresponding global estimator were evaluated through a simulation study.Analysis and evaluation are presented.
基金supported by the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202002)the Natural Science Foundation of Jiangsu Province(Grant No.BK20180413)+4 种基金the National Natural Science Foundation of China(Grant Nos.11801269,12071216)supported by Science Challenge Project(Grant No.TZ2018002)National Science and TechnologyMajor Project(J2019-II-0007-0027)supported by the China Postdoctoral Science Foundation(Grant No.2020M670116)the Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems(Grant No.202001).
文摘In this paper,we present a quadratic auxiliary variable approach to develop a new class of energy-preserving Runge-Kutta methods for the Korteweg-de Vries equation.The quadratic auxiliary variable approach is first proposed to reformulate the original model into an equivalent system,which transforms the energy conservation law of the Korteweg-de Vries equation into two quadratic invariants of the reformulated system.Then the symplectic Runge-Kutta methods are directly employed for the reformulated model to arrive at a new kind of time semi-discrete schemes for the original problem.Under consistent initial conditions,the proposed methods are rigorously proved to maintain the original energy conservation law of the Korteweg-de Vries equation.In addition,the Fourier pseudo-spectral method is used for spatial discretization,resulting in fully discrete energy-preserving schemes.To implement the proposed methods effectively,we present a very efficient iterative technique,which not only greatly saves the calculation cost,but also achieves the purpose of practically preserving structure.Ample numerical results are addressed to confirm the expected order of accuracy,conservative property and efficiency of the proposed algorithms.