In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen...In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.展开更多
This paper presents Modified Chebyshev-Picard Iteration(MCPI)methods for long-term integration of the coupled orbit and attitude dynamics.Although most orbit predictions for operational satellites have assumed that th...This paper presents Modified Chebyshev-Picard Iteration(MCPI)methods for long-term integration of the coupled orbit and attitude dynamics.Although most orbit predictions for operational satellites have assumed that the attitude dynamics is decoupled from the orbit dynamics,the fully coupled dynamics is required for the solutions of uncontrolled space debris and space objects with high area-to-mass ratio,for which cross sectional area is constantly changing leading to significant change on the solar radiation pressure and atmospheric drag.MCPI is a set of methods for solution of initial value problems and boundary value problems.The methods refine an orthogonal function approximation of long-time-interval segments of state trajectories iteratively by fusing Chebyshev polynomials with the classical Picard iteration and have been applied to multiple challenging aerospace problems.Through the studies on integrating a torque-free rigid body rotation and a long-term integration of the coupled orbit-attitude dynamics through the effect of solar radiation pressure,MCPI methods are shown to achieve several times speedup over the Runge-Kutta 7(8)methods with several orders of magnitudes of better accuracy.MCPI methods are further optimized by integrating the decoupled dynamics at the beginning of the iteration and coupling the full dynamics when the attitude solutions and orbit solutions are converging during the iteration.The approach of decoupling and then coupling during iterations provides a unique and promising perspective on the way to warm start the solution process for the longterm integration of the coupled orbit-attitude dynamics.Furthermore,an attractive feature of MCPI in maintaining the unity constraint for the integration of quaternions within machine accuracy is illustrated to be very appealing.展开更多
The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of dril...The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.展开更多
We present a Hermitian and skew-Herrnitian splitting （HSS） iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi- definite matrices. The unconditional...We present a Hermitian and skew-Herrnitian splitting （HSS） iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi- definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.展开更多
This paper presents optimum an one-parameter iteration (OOPI) method and a multi-parameter iteration direct (MPID) method for efficiently solving linear algebraic systems with low order matrix A and high order matrix ...This paper presents optimum an one-parameter iteration (OOPI) method and a multi-parameter iteration direct (MPID) method for efficiently solving linear algebraic systems with low order matrix A and high order matrix B: Y = (A B)Y + Φ. On parallel computers (also on serial computer) the former will be efficient, even very efficient under certain conditions, the latter will be universally very efficient.展开更多
For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 ...For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 （2012） 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting （GLHSS） iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the con- vergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.展开更多
Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyc...Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.展开更多
For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observat...For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.展开更多
This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional ...This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.展开更多
We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction(FSI).The solver is based on a modeling approach that uses the velocity and pressure as the primitive ...We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction(FSI).The solver is based on a modeling approach that uses the velocity and pressure as the primitive variables,which offers a bridge between computational fluid dynamics(CFD)and computational structural dynamics.The spatiotemporal discretization leverages the variational multiscale formulation and the generalized-αmethod as a means of providing a robust discrete scheme.In particular,the time integration scheme does not suffer from the overshoot phenomenon and optimally dissipates high-frequency spurious modes in both subproblems of FSI.Based on the chosen fully implicit scheme,we systematically develop a combined suite of nonlinear and linear solver strategies.Invoking a block factorization of the Jacobian matrix,the Newton-Raphson procedure is reduced to solving two smaller linear systems in the multi-corrector stage.The first is of the elliptic type,indicating that the algebraic multigrid method serves as a well-suited option.The second exhibits a two-by-two block structure that is analogous to the system arising in CFD.Inspired by prior studies,the additive Schwarz domain decomposition method and the block-factorization-based preconditioners are invoked to address the linear problem.Since the number of unknowns matches in both subdomains,it is straightforward to balance loads when parallelizing the algorithm for distributed-memory architectures.We use two representative FSI benchmarks to demonstrate the robustness,efficiency,and scalability of the overall FSI solver framework.In particular,it is found that the developed FSI solver is comparable to the CFD solver in several aspects,including fixed-size and isogranular scalability as well as robustness.展开更多
This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of no...This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.展开更多
Currently,the main idea of iterative rendering methods is to allocate a fixed number of samples to pixels that have not been fully rendered by calculating the completion rate.It is obvious that this strategy ignores t...Currently,the main idea of iterative rendering methods is to allocate a fixed number of samples to pixels that have not been fully rendered by calculating the completion rate.It is obvious that this strategy ignores the changes in pixel values during the previous rendering process,which may result in additional iterative operations.展开更多
A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conce...A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.展开更多
A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode...A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order...In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.展开更多
The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Househo...The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.展开更多
In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-m...In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.展开更多
One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some un...One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.展开更多
For over half a century,numerical integration methods based on finite difference,such as the Runge-Kutta method and the Euler method,have been popular and widely used for solving orbit dynamic problems.In general,a sm...For over half a century,numerical integration methods based on finite difference,such as the Runge-Kutta method and the Euler method,have been popular and widely used for solving orbit dynamic problems.In general,a small integration step size is always required to suppress the increase of the accumulated computation error,which leads to a relatively slow computation speed.Recently,a collocation iteration method,approximating the solutions of orbit dynamic problems iteratively,has been developed.This method achieves high computation accuracy with extremely large step size.Although efficient,the collocation iteration method suffers from two limitations:(A)the computational error limit of the approximate solution is not clear;(B)extensive trials and errors are always required in tuning parameters.To overcome these problems,the influence mechanism of how the dynamic problems and parameters affect the error limit of the collocation iteration method is explored.On this basis,a parameter adjustment method known as the“polishing method”is proposed to improve the computation speed.The method proposed is demonstrated in three typical orbit dynamic problems in aerospace engineering:a low Earth orbit propagation problem,a Molniya orbit propagation problem,and a geostationary orbit propagation problem.Numerical simulations show that the proposed polishing method is faster and more accurate than the finite-difference-based method and the most advanced collocation iteration method.展开更多
基金The NSF(0611005)of Jiangxi Province and the SF(2007293)of Jiangxi Provincial Education Department.
文摘In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.
文摘This paper presents Modified Chebyshev-Picard Iteration(MCPI)methods for long-term integration of the coupled orbit and attitude dynamics.Although most orbit predictions for operational satellites have assumed that the attitude dynamics is decoupled from the orbit dynamics,the fully coupled dynamics is required for the solutions of uncontrolled space debris and space objects with high area-to-mass ratio,for which cross sectional area is constantly changing leading to significant change on the solar radiation pressure and atmospheric drag.MCPI is a set of methods for solution of initial value problems and boundary value problems.The methods refine an orthogonal function approximation of long-time-interval segments of state trajectories iteratively by fusing Chebyshev polynomials with the classical Picard iteration and have been applied to multiple challenging aerospace problems.Through the studies on integrating a torque-free rigid body rotation and a long-term integration of the coupled orbit-attitude dynamics through the effect of solar radiation pressure,MCPI methods are shown to achieve several times speedup over the Runge-Kutta 7(8)methods with several orders of magnitudes of better accuracy.MCPI methods are further optimized by integrating the decoupled dynamics at the beginning of the iteration and coupling the full dynamics when the attitude solutions and orbit solutions are converging during the iteration.The approach of decoupling and then coupling during iterations provides a unique and promising perspective on the way to warm start the solution process for the longterm integration of the coupled orbit-attitude dynamics.Furthermore,an attractive feature of MCPI in maintaining the unity constraint for the integration of quaternions within machine accuracy is illustrated to be very appealing.
基金supported by the National Natural Science Foundation of China(52174003,52374008).
文摘The complex vibration directly affects the dynamic safety of drill string in ultra-deep wells and extra-deep wells.It is important to understand the dynamic characteristics of drill string to ensure the safety of drill string.Due to the super slenderness ratio of drill string,strong nonlinearity implied in dynamic analysis and the complex load environment,dynamic simulation of drill string faces great challenges.At present,many simulation methods have been developed to analyze drill string dynamics,and node iteration method is one of them.The node iteration method has a unique advantage in dealing with the contact characteristics between drill string and borehole wall,but its drawback is that the calculation consumes a considerable amount of time.This paper presents a dynamic simulation method of drilling string in extra-deep well based on successive over-relaxation node iterative method(SOR node iteration method).Through theoretical analysis and numerical examples,the correctness and validity of this method were verified,and the dynamics characteristics of drill string in extra-deep wells were calculated and analyzed.The results demonstrate that,in contrast to the conventional node iteration method,the SOR node iteration method can increase the computational efficiency by 48.2%while achieving comparable results.And the whirl trajectory of the extra-deep well drill string is extremely complicated,the maximum rotational speed downhole is approximately twice the rotational speed on the ground.The dynamic torque increases rapidly at the position of the bottom stabilizer,and the lateral vibration in the middle and lower parts of drill string is relatively intense.
文摘We present a Hermitian and skew-Herrnitian splitting （HSS） iteration method for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi- definite matrices. The unconditional convergence of the HSS iteration method is proved and an upper bound on the convergence rate is derived. Moreover, to reduce the computing cost, we establish an inexact variant of the HSS iteration method and analyze its convergence property in detail. Numerical results show that the HSS iteration method and its inexact variant are efficient and robust solvers for this class of continuous Sylvester equations.
基金national natural science foundation of China !(19671039).
文摘This paper presents optimum an one-parameter iteration (OOPI) method and a multi-parameter iteration direct (MPID) method for efficiently solving linear algebraic systems with low order matrix A and high order matrix B: Y = (A B)Y + Φ. On parallel computers (also on serial computer) the former will be efficient, even very efficient under certain conditions, the latter will be universally very efficient.
基金We would like to express our sincere gratitude to the anonymous referees whose constructive comments have the presentation of this paper greatly improved. The work was supported by the National Natural Science Foundation （No.11171371 and No.11101195）.
文摘For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 （2012） 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting （GLHSS） iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the con- vergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.
文摘Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.
基金co-supported by the National Natural Science Foundation of China(No.62303246,No.62103204)the China Postdoctoral Science Foundation(No.2023M731788)。
文摘For nonlinear state estimation driven by non-Gaussian noise,the estimator is required to be updated iteratively.Since the iterative update approximates a linear process,it fails to capture the nonlinearity of observation models,and this further degrades filtering accuracy and consistency.Given the flaws of nonlinear iteration,this work incorporates a recursive strategy into generalized M-estimation rather than the iterative strategy.The proposed algorithm extends nonlinear recursion to nonlinear systems using the statistical linear regression method.The recursion allows for the gradual release of observation information and consequently enables the update to proceed along the nonlinear direction.Considering the correlated state and observation noise induced by recursions,a separately reweighting strategy is adopted to build a robust nonlinear system.Analogous to the nonlinear recursion,a robust nonlinear recursive update strategy is proposed,where the associated covariances and the observation noise statistics are updated recursively to ensure the consistency of observation noise statistics,thereby completing the nonlinear solution of the robust system.Compared with the iterative update strategies under non-Gaussian observation noise,the recursive update strategy can facilitate the estimator to achieve higher filtering accuracy,stronger robustness,and better consistency.Therefore,the proposed strategy is more suitable for the robust nonlinear filtering framework.
基金funded by the Research,Development,and Innovation Authority(RDIA)-Kingdom of Saudi Arabia-with grant number 12803-baha-2023-BU-R-3-1-EI.
文摘This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.
基金This work was supported by the National Natural Science Foundation of China(Grant No.12172160)Shenzhen Science and Technology Program(Grant No.JCYJ20220818100600002)+1 种基金South-ern University of Science and Technology(Grant No.Y01326127)the Department of Science and Technology of Guangdong Province(Grant Nos.2020B1212030001 and 2021QN020642).
文摘We propose a suite of strategies for the parallel solution of fully implicit monolithic fluid-structure interaction(FSI).The solver is based on a modeling approach that uses the velocity and pressure as the primitive variables,which offers a bridge between computational fluid dynamics(CFD)and computational structural dynamics.The spatiotemporal discretization leverages the variational multiscale formulation and the generalized-αmethod as a means of providing a robust discrete scheme.In particular,the time integration scheme does not suffer from the overshoot phenomenon and optimally dissipates high-frequency spurious modes in both subproblems of FSI.Based on the chosen fully implicit scheme,we systematically develop a combined suite of nonlinear and linear solver strategies.Invoking a block factorization of the Jacobian matrix,the Newton-Raphson procedure is reduced to solving two smaller linear systems in the multi-corrector stage.The first is of the elliptic type,indicating that the algebraic multigrid method serves as a well-suited option.The second exhibits a two-by-two block structure that is analogous to the system arising in CFD.Inspired by prior studies,the additive Schwarz domain decomposition method and the block-factorization-based preconditioners are invoked to address the linear problem.Since the number of unknowns matches in both subdomains,it is straightforward to balance loads when parallelizing the algorithm for distributed-memory architectures.We use two representative FSI benchmarks to demonstrate the robustness,efficiency,and scalability of the overall FSI solver framework.In particular,it is found that the developed FSI solver is comparable to the CFD solver in several aspects,including fixed-size and isogranular scalability as well as robustness.
文摘This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.
基金supported partially by the National Natural Science Foundation of China(No.U19A2063)the Jilin Provincial Science&Technology Development Program of China(No.20230201080GX)。
文摘Currently,the main idea of iterative rendering methods is to allocate a fixed number of samples to pixels that have not been fully rendered by calculating the completion rate.It is obvious that this strategy ignores the changes in pixel values during the previous rendering process,which may result in additional iterative operations.
文摘A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90111011 and 10471039）, the National Key Basic Research Special Foundation of China （Grant Nos 2003CB415101-03 and 2004CB418304）, the Key Basic Research Foundation of the Chinese Academy of Sciences （Grant No KZCX3-SW-221） and in part by E-Institutes of Shanghai Municipal Education Commission （Grant No N.E03004）.
文摘A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.
基金This research was supported by Universiti Kebangsaan Malaysia under research grant GUP-2019-033.
文摘The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.
文摘In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.
基金National Natural Science Foundation of China under Grant No.10172056
文摘One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.
基金This study was co-supported by the National Key Research and Development Program of China(No.2021YFA0717100)the National Natural Science Foundation of China(Nos.12072270,U2013206).
文摘For over half a century,numerical integration methods based on finite difference,such as the Runge-Kutta method and the Euler method,have been popular and widely used for solving orbit dynamic problems.In general,a small integration step size is always required to suppress the increase of the accumulated computation error,which leads to a relatively slow computation speed.Recently,a collocation iteration method,approximating the solutions of orbit dynamic problems iteratively,has been developed.This method achieves high computation accuracy with extremely large step size.Although efficient,the collocation iteration method suffers from two limitations:(A)the computational error limit of the approximate solution is not clear;(B)extensive trials and errors are always required in tuning parameters.To overcome these problems,the influence mechanism of how the dynamic problems and parameters affect the error limit of the collocation iteration method is explored.On this basis,a parameter adjustment method known as the“polishing method”is proposed to improve the computation speed.The method proposed is demonstrated in three typical orbit dynamic problems in aerospace engineering:a low Earth orbit propagation problem,a Molniya orbit propagation problem,and a geostationary orbit propagation problem.Numerical simulations show that the proposed polishing method is faster and more accurate than the finite-difference-based method and the most advanced collocation iteration method.
