Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced va...Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.展开更多
Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremend...Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.展开更多
A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method ...A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.展开更多
Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing ...Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.展开更多
In this paper,we study the hyperstability for the general linear equation f(ax+by)=Af(x)+Bf(y)in the setting of complete quasi-2-Banach spaces.We first extend the main fixed point result of Brzdek and Ciepliński(Acta...In this paper,we study the hyperstability for the general linear equation f(ax+by)=Af(x)+Bf(y)in the setting of complete quasi-2-Banach spaces.We first extend the main fixed point result of Brzdek and Ciepliński(Acta Mathematica Scientia,2018,38 B(2):377-390)to quasi-2-Banach spaces by defining an equivalent quasi-2-Banach space.Then we use this result to generalize the main results on the hyperstability for the general linear equation in quasi-2-Banach spaces.Our results improve and generalize many results of literature.展开更多
Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this pap...Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this paper:(i)(λⅠ_n-A)x=b,x∈K,and(ii)(A-λⅠ_n)x=b,x∈K.We obtain several equivalent conditions for the solvability of the first equation.展开更多
Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equation...Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equations and the possibilistic linear programming problems and present an alternative method of solving the systems of fuzzy linear equations.展开更多
The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or ve...The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.展开更多
This paper deals with the distributed solving problem of a specific class of linear algebraic equations(LAEs)with block Toeplitz structures.To reduce the communication burden and achieve computation efficiency,a distr...This paper deals with the distributed solving problem of a specific class of linear algebraic equations(LAEs)with block Toeplitz structures.To reduce the communication burden and achieve computation efficiency,a distributed iterative algorithm from the communication-efficient perspective is proposed by incorporating the specific structure of the coefficient matrix tied to any given LAE over a multi-agent network.Each agent possesses a state vector of size smaller than the dimensions of unknown variables related to the LAE and receives information from its neighbors.It is shown that the presented distributed iterative algorithm can solve the specific class of LAEs without requiring any initialization conditions,irrespective of whether it admits a unique solution or multiple solutions.Moreover,an equivalent relation is established between the problem of solving LAEs and the tracking problem of iterative learning control(ILC)systems.The proposed distributed iterative algorithm is leveraged to obtain the distributed control law for ILC systems to realize the tracking objective.Theoretical guarantees are provided for our developed solution results of LAEs,and the effectiveness of them is also verified through simulation examples.展开更多
Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further ...Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25).展开更多
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
In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the g...In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.展开更多
This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either...This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.展开更多
Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback com...Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback combination of the agent's own state and neighbors' output,which can achieve exponential output consensus through intermittent communication. The controller is obtained by solving two linear matrix equations, and Zeno behavior is excluded.展开更多
Wave shoaling,which involves an increase in wave amplitude due to changes in water depth,can damage shore-lines.To mitigate this damage,we propose using porous structures such as mangrove forests.In this study,we use ...Wave shoaling,which involves an increase in wave amplitude due to changes in water depth,can damage shore-lines.To mitigate this damage,we propose using porous structures such as mangrove forests.In this study,we use a mathematical model to examine how mangroves,acting as porous breakwater,can reduce wave shoaling amplitude.The shallow water equations are used as the governing equations and are modified to account for the presence of porous media.To measure the wave reduction generated by the porous media,the wave transmis-sion coefficient is estimated using analytical and numerical approaches.The separation of variables method and the staggered finite volume method are utilized for each approach,respectively.The numerical results are then validated against the previously obtained analytical solutions.We then vary the friction and porosity parame-ters-determined by the presence and extent of porous media,to evaluate their effectiveness in reducing wave shoaling.展开更多
Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving no...Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.展开更多
Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterativ...Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.展开更多
Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. Ho...Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.62172268 and 62302289the Shanghai Science and Technology Project under Grant Nos.21JC1402800 and 23YF1416200。
文摘Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.
文摘Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations.The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications.So,practical solvers for systems of linear and nonlinear equations based on multi graphic process units（GPUs）are proposed in order to accelerate the solving process.In the linear and nonlinear solvers,the preconditioned bi-conjugate gradient stable（PBi-CGstab）method and the Inexact Newton method are used to achieve the fast and stable convergence behavior.Multi-GPUs are utilized to obtain more data storage that large size problems need.
基金Project supported by the National Natural Science Foundation of China (Nos. 10232040, 10572002 and 10572003)
文摘A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests.
基金Project supported by the National Natural Science Foundation of China(Nos.5130926141030747+3 种基金41102181and 51121005)the National Basic Research Program of China(973 Program)(No.2011CB013503)the Young Teachers’ Initial Funding Scheme of Sun Yat-sen University(No.39000-1188140)
文摘Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.
基金AISTDF,DST India for the research grant vide project No.CRD/2018/000017。
文摘In this paper,we study the hyperstability for the general linear equation f(ax+by)=Af(x)+Bf(y)in the setting of complete quasi-2-Banach spaces.We first extend the main fixed point result of Brzdek and Ciepliński(Acta Mathematica Scientia,2018,38 B(2):377-390)to quasi-2-Banach spaces by defining an equivalent quasi-2-Banach space.Then we use this result to generalize the main results on the hyperstability for the general linear equation in quasi-2-Banach spaces.Our results improve and generalize many results of literature.
文摘Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this paper:(i)(λⅠ_n-A)x=b,x∈K,and(ii)(A-λⅠ_n)x=b,x∈K.We obtain several equivalent conditions for the solvability of the first equation.
文摘Many systems of fuzzy linear equations do not have solutions when the solution concept is based on α cuts and interval arithmetic. In this paper,we establish the relations between the systems of fuzzy linear equations and the possibilistic linear programming problems and present an alternative method of solving the systems of fuzzy linear equations.
文摘The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.
基金supported by the National Natural Science Foundation of China under Grant Nos.U2333215,62273018,and U2133210。
文摘This paper deals with the distributed solving problem of a specific class of linear algebraic equations(LAEs)with block Toeplitz structures.To reduce the communication burden and achieve computation efficiency,a distributed iterative algorithm from the communication-efficient perspective is proposed by incorporating the specific structure of the coefficient matrix tied to any given LAE over a multi-agent network.Each agent possesses a state vector of size smaller than the dimensions of unknown variables related to the LAE and receives information from its neighbors.It is shown that the presented distributed iterative algorithm can solve the specific class of LAEs without requiring any initialization conditions,irrespective of whether it admits a unique solution or multiple solutions.Moreover,an equivalent relation is established between the problem of solving LAEs and the tracking problem of iterative learning control(ILC)systems.The proposed distributed iterative algorithm is leveraged to obtain the distributed control law for ILC systems to realize the tracking objective.Theoretical guarantees are provided for our developed solution results of LAEs,and the effectiveness of them is also verified through simulation examples.
文摘Let a_(1),a_(2),a_(3)be nonzero integers with gcd(a_(1),a_(2),a_(3))=1,and let k be any positive integer,K=max[3,|a_(1)|,|a_(2)|,|a_(3)|,k].Suppose that l_(1),l_(2),l_(3)are integers each coprime to k.Suppose further that b is any integer satisfying some necessary congruent conditions.The solvability of linear equation a_(1)p_(1)+a_(2)p_(2)+a_(3)p_(3)=b(p_(j)=l_(j)(mod k),1≤j≤3)with prime variables pi,p_(2),ps is investigated.It is proved that if ai,a_(2),a_(3)are all positive,then the above equation is solvable whenever b≥K^(25);if a,a_(2),a_(3)are not all of the same sign,then the above equation has a solution p_(1),p_(2),p_(3)satisfying max(p_(1),p_(2),p_(3))≤3|b|+K^(25).
基金supported by the National Natural Science Foundation of China(Grant No.12031004 and Grant No.12271474,61877054)the Fundamental Research Foundation for the Central Universities(Project No.K20210337)+1 种基金the Zhejiang University Global Partnership Fund,188170+194452119/003partially funded by a state task of Russian Fundamental Investigations(State Registration No.FFSG-2024-0002)。
文摘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.
基金supported by the Simons Foundation:Collaboration Grantssupported by the AFOSR grant FA9550-18-1-0383.
文摘In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.
基金supported by the NSF under Grant DMS-2208391sponsored by the NSF under Grant DMS-1753581.
文摘This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.
基金supported by the National Science and Technology Innovation 2030-Major Program(2022ZD 0115403)the National Natural Science Foundation of China(61991414)+1 种基金Chongqing Natural Science Foundation(CSTB2023NSCQJQX0018)Beijing Natural Science Foundation(L221005)
文摘Dear Editor,This letter studies output consensus problem of heterogeneous linear multiagent systems over directed graphs. A novel adaptive dynamic event-triggered controller is presented based only on the feedback combination of the agent's own state and neighbors' output,which can achieve exponential output consensus through intermittent communication. The controller is obtained by solving two linear matrix equations, and Zeno behavior is excluded.
基金support from Program Riset Kolaborasi Indonesia(RKI)2024(Grant No.1841/IT1.B07.1/TA.00/2024).
文摘Wave shoaling,which involves an increase in wave amplitude due to changes in water depth,can damage shore-lines.To mitigate this damage,we propose using porous structures such as mangrove forests.In this study,we use a mathematical model to examine how mangroves,acting as porous breakwater,can reduce wave shoaling amplitude.The shallow water equations are used as the governing equations and are modified to account for the presence of porous media.To measure the wave reduction generated by the porous media,the wave transmis-sion coefficient is estimated using analytical and numerical approaches.The separation of variables method and the staggered finite volume method are utilized for each approach,respectively.The numerical results are then validated against the previously obtained analytical solutions.We then vary the friction and porosity parame-ters-determined by the presence and extent of porous media,to evaluate their effectiveness in reducing wave shoaling.
基金Supported by National Natural Science Foundation of China (Grant No. 10771040)Guangxi Science Foundation (Grant No. 0832052)Guangxi University for Nationalities Youth Foundation (Grant No. 2007QN24)
文摘Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations （SSLE） algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.
基金Supported by the National Natural Science Foundation of China(61272300)
文摘Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60873249, 60973142)the National High-Tech Research & Development Program of China (Grant Nos. 2008AA10Z419, 2009AA011906)the Project Funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua University
文摘Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.
