The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are est...The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.展开更多
The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel(t−s)^(−μ) with 0<μ<1.In this work,we consider the case when the underlying...The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel(t−s)^(−μ) with 0<μ<1.In this work,we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth.We provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.The numerical examples are given to illustrate the theoretical results.展开更多
We describe the application of the spectral method to delay integro-differential equations with proportional delays. It is shown that the resulting numerical solutions exhibit the spectral convergence order. Extension...We describe the application of the spectral method to delay integro-differential equations with proportional delays. It is shown that the resulting numerical solutions exhibit the spectral convergence order. Extensions to equations with more general （nonlinear） vanishing delays are also discussed.展开更多
In this paper,an initial boundary value problem of the space-time fractional diffusion equation is studied.Both temporal and spatial directions for this equation are discreted by the Galerkin spectral methods.And then...In this paper,an initial boundary value problem of the space-time fractional diffusion equation is studied.Both temporal and spatial directions for this equation are discreted by the Galerkin spectral methods.And then based on the discretization scheme,reliable a posteriori error estimates for the spectral approximation are derived.Some numerical examples are presented to verify the validity and applicability of the derived a posteriori error estimator.展开更多
We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear ...We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear problems. Some numerical results and error estimates of these methods are given.展开更多
We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares func...We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.展开更多
In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular different...In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular differential equations. Then we present the generalized Jacobi quasi-orthogonal approximation and its applica- tions to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions. We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains. Next, we consider the Hermite spectral method and the generalized Hermite spec- tral method with their applications. Finally, we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defined on unbounded domains. We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.展开更多
Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data,the initial conditions and the operator coe...Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data,the initial conditions and the operator coefficients.Sharp/strict maximum principles insomuch of fundamental importance for the continuous problem often do not persist under numerical discretization.A lot of past research concentrates on designing fine numerical schemes which preserves the sharp maximum principles especially for nonlinear problems.However these sharp principles not only sometimes introduce unwanted stringent conditions on the numerical schemes but also completely leaves many powerful frequency-based methods unattended and rarely analyzed directly in the sharp ma-ximum norm topology.A prominent example is the spectral methods in the family of weighted residual methods.In this work we introduce and develop a new framework of almost sharp maximum principles which allow the numerical solutions to deviate from the sharp bound by a controllable discretization error:we call them effective maximum principles.We showcase the analysis for the classical Fourier spectral methods including Fourier Galerkin and Fourier collocation in space with forward Euler in time or second order Strang splitting.The model equations include the Allen-Cahn equations with double well potential,the Burgers equation and the Navier-Stokes equations.We give a comprehensive proof of the effective maximum principles under very general parametric conditions.展开更多
In this paper,efficient numerical scheme is proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water wave.By using the Caputo fractional derivative definition...In this paper,efficient numerical scheme is proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water wave.By using the Caputo fractional derivative definition to approximate the nonlocal fractional operator,finite difference method in time and spectral method in space are constructed for the considered model.The proposed method employs known 5/2 order scheme for fractional derivative and a mixed linearization for the nonlinear term.The analysis shows that the proposed numerical scheme is unconditionally stable and error estimates are provided to predict that the second order backward differentiation plus 5/2 order scheme converges with order 2 in time,and spectral accuracy in space.Several numerical results are provided to verify the efficiency and accuracy of our theoretical claims.Finally,the decay rate of solutions are investigated.展开更多
An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained ex...An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained explicitly which plays an important role in the numerical analysis.And a sharp estimate on the algebraic system's condition number is established which behaves as N4s with respect to the polynomial degree N,where 2s is the fractional derivative order.The regularity estimate of solutions to source problems of the fractional Laplacian in arbitrary dimensions is firstly investigated in weighted Sobolev spaces.Then the regularity of eigenfunctions of the fractional Laplacian eigenvalue problem is readily derived.Meanwhile,rigorous error estimates of the eigenvalues and eigenvectors are ob-tained.Numerical experiments are presented to demonstrate the accuracy and efficiency and to validate the theoretical results.展开更多
In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)deriva...In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.展开更多
This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the acc...This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.展开更多
The behavior of buoyancy-driven magnetohydrodynamic(MHD)nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling,nuclear reactors,and me...The behavior of buoyancy-driven magnetohydrodynamic(MHD)nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling,nuclear reactors,and metallurgical processes.This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe3O4 nanofluid influenced by magnetic field-dependent viscosity and thermal radiation,as it interacts with a vertically stretching sheet under dissipative conditions.To manage the inherent nonlinearities,Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms.These reduced equations are then solved via the Spectral Quasi-Linearization Method(SQLM),ensuring high accuracy and computational efficiency.The analysis comprehensively explores the impact of key parameters-including mixed convection intensity,magnetic field strength,Casson fluid properties,temperature-dependent viscosity,thermal radiation,and viscous dissipation(Eckert number)-on flow characteristics and heat transfer rates.Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport,while buoyancy effects enhance heat transfer but lower shear stress on the surface.This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids,advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.展开更多
The spectral methods and ice-induced fatigue analysis are discussed based on Miner＇s linear cumulative fatigue hypothesis and S-N curve data. According to the long-term data of full-scale tests on the platforms in th...The spectral methods and ice-induced fatigue analysis are discussed based on Miner＇s linear cumulative fatigue hypothesis and S-N curve data. According to the long-term data of full-scale tests on the platforms in the Bohai Sea, the ice force spectrum of conical structures and the fatigue environmental model are established. Moreover, the finite element model of JZ20-2MSW platform, an example of ice-induced fatigue analysis, is built with ANSYS software. The mode analysis and dynamic analysis in frequency domain under all kinds of ice fatigue work conditions are carded on, and the fatigue life of the structure is estimated in detail. The methods in this paper can be helpful in ice-induced fatigue analysis of ice-resistant platforms.展开更多
We analyzed the infrared 0R）-near infrared （NIR） 2D correlation spectra of drugs perturbed by temperature. By identification of functional groups by IR spectrum and by the correlation analysis of IR-NIR spectrum, w...We analyzed the infrared 0R）-near infrared （NIR） 2D correlation spectra of drugs perturbed by temperature. By identification of functional groups by IR spectrum and by the correlation analysis of IR-NIR spectrum, we identified the characteristic spectral bands that were closely related to the structure of a drug substance of interest. These characteristic spectral bands were relatively less interfered by other ingredients for analysis by the NIR correlation coefficient method. With these characteristic spectral bands, the accuracy of screening illegally added Sildenafil citrate, Tadalafil and Metforrnin hydrochloride in Chinese patent drugs and healthcare products reached about 90%, which met the requirements of rapid screening.展开更多
The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution ...The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.展开更多
This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating ...This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established.This formula is expressed in terms of a certain terminating hypergeometric function of the type_(4)F_(3)(1).This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3 F 2(1)which can be summed with the aid of Watson’s identity.Six illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.展开更多
In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transforma...In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.展开更多
In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident bou...In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.展开更多
The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical ...The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.展开更多
基金the Science Foundation of the Science and Technology Commission of Shanghai Municipality(No.075105118)the Shanghai Leading Academic Discipline Project(No.T0401)the Fund for E-institute of Shanghai Universities(No.E03004)
文摘The Laguerre spectral and pseudospectral methods are investigated for multidimensional nonlinear partial differential equations. Some results on the modified Laguerre orthogonal approximation and interpolation are established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified Laguerre spectral and pseudospectral methods are proposed for two-dimensional Logistic equation. The stability and convergence of the suggested schemes are proved. Numerical results demonstrate the high accuracy of these approaches.
基金This work is supported by the Foundation for Talent Introduction of Guangdong Provincial University,Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2008)National Science Foundation of China(10971074).
文摘The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel(t−s)^(−μ) with 0<μ<1.In this work,we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth.We provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.The numerical examples are given to illustrate the theoretical results.
文摘We describe the application of the spectral method to delay integro-differential equations with proportional delays. It is shown that the resulting numerical solutions exhibit the spectral convergence order. Extensions to equations with more general （nonlinear） vanishing delays are also discussed.
基金supported by the State Key Program of National Natural Science Foundation of China(No.11931003)National Natural Science Foundation of China(Nos.41974133,11671157 and 11971410)supported by the Innovation Project of Graduate School of South China Normal University(No.2018LKXM008).
文摘In this paper,an initial boundary value problem of the space-time fractional diffusion equation is studied.Both temporal and spatial directions for this equation are discreted by the Galerkin spectral methods.And then based on the discretization scheme,reliable a posteriori error estimates for the spectral approximation are derived.Some numerical examples are presented to verify the validity and applicability of the derived a posteriori error estimator.
文摘We take the two dimensional vorticity equations as models to describe spectral methods and their combinations with finite difference methods or finite element methods, which are applicable to other similar nonlinear problems. Some numerical results and error estimates of these methods are given.
文摘We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.
基金supported by National Natural Science Foundation of China(Grant No.11171227)Fund for Doctoral Authority of China(Grant No.20123127110001)+1 种基金Fund for E-institute of Shanghai Universities(Grant No.E03004)Leading Academic Discipline Project of Shanghai Municipal Education Commission(Grant No.J50101)
文摘In this paper, we review some results on the spectral methods. We first consider the Jacobi spectral method and the generalized Jacobi spectral method for various problems, including degenerated and singular differential equations. Then we present the generalized Jacobi quasi-orthogonal approximation and its applica- tions to the spectral element methods for high order problems with mixed inhomogeneous boundary conditions. We also discuss the related spectral methods for non-rectangular domains and the irrational spectral methods for unbounded domains. Next, we consider the Hermite spectral method and the generalized Hermite spec- tral method with their applications. Finally, we consider the Laguerre spectral method and the generalized Laguerre spectral method for many problems defined on unbounded domains. We also present the generalized Laguerre quasi-orthogonal approximation and its applications to certain problems of non-standard type and exterior problems.
文摘Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data,the initial conditions and the operator coefficients.Sharp/strict maximum principles insomuch of fundamental importance for the continuous problem often do not persist under numerical discretization.A lot of past research concentrates on designing fine numerical schemes which preserves the sharp maximum principles especially for nonlinear problems.However these sharp principles not only sometimes introduce unwanted stringent conditions on the numerical schemes but also completely leaves many powerful frequency-based methods unattended and rarely analyzed directly in the sharp ma-ximum norm topology.A prominent example is the spectral methods in the family of weighted residual methods.In this work we introduce and develop a new framework of almost sharp maximum principles which allow the numerical solutions to deviate from the sharp bound by a controllable discretization error:we call them effective maximum principles.We showcase the analysis for the classical Fourier spectral methods including Fourier Galerkin and Fourier collocation in space with forward Euler in time or second order Strang splitting.The model equations include the Allen-Cahn equations with double well potential,the Burgers equation and the Navier-Stokes equations.We give a comprehensive proof of the effective maximum principles under very general parametric conditions.
基金The research of this author is partially supported by NSF of China(51661135011 and 91630204).
文摘In this paper,efficient numerical scheme is proposed for solving the water wave model with nonlocal viscous term that describe the propagation of surface water wave.By using the Caputo fractional derivative definition to approximate the nonlocal fractional operator,finite difference method in time and spectral method in space are constructed for the considered model.The proposed method employs known 5/2 order scheme for fractional derivative and a mixed linearization for the nonlinear term.The analysis shows that the proposed numerical scheme is unconditionally stable and error estimates are provided to predict that the second order backward differentiation plus 5/2 order scheme converges with order 2 in time,and spectral accuracy in space.Several numerical results are provided to verify the efficiency and accuracy of our theoretical claims.Finally,the decay rate of solutions are investigated.
基金supported by the National Natural Science Foundation of China(Grant No.12101325)and by the NUPTSF(Grant No.NY220162)The second author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,11971016)+1 种基金The third author was supported by the National Natural Science Foundation of China(Grant No.12131005)The fifth author was supported by the National Natural Science Foundation of China(Grant Nos.12131005,U2230402).
文摘An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained explicitly which plays an important role in the numerical analysis.And a sharp estimate on the algebraic system's condition number is established which behaves as N4s with respect to the polynomial degree N,where 2s is the fractional derivative order.The regularity estimate of solutions to source problems of the fractional Laplacian in arbitrary dimensions is firstly investigated in weighted Sobolev spaces.Then the regularity of eigenfunctions of the fractional Laplacian eigenvalue problem is readily derived.Meanwhile,rigorous error estimates of the eigenvalues and eigenvectors are ob-tained.Numerical experiments are presented to demonstrate the accuracy and efficiency and to validate the theoretical results.
基金extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/174/46.
文摘In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.
基金supported by the Advance Research Project of Civil Aerospace Technology(Grant No.D020304)National Nat-ural Science Foundation of China(Grant Nos.52205257 and U22B2083).
文摘This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.
文摘The behavior of buoyancy-driven magnetohydrodynamic(MHD)nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling,nuclear reactors,and metallurgical processes.This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe3O4 nanofluid influenced by magnetic field-dependent viscosity and thermal radiation,as it interacts with a vertically stretching sheet under dissipative conditions.To manage the inherent nonlinearities,Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms.These reduced equations are then solved via the Spectral Quasi-Linearization Method(SQLM),ensuring high accuracy and computational efficiency.The analysis comprehensively explores the impact of key parameters-including mixed convection intensity,magnetic field strength,Casson fluid properties,temperature-dependent viscosity,thermal radiation,and viscous dissipation(Eckert number)-on flow characteristics and heat transfer rates.Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport,while buoyancy effects enhance heat transfer but lower shear stress on the surface.This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids,advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.
基金The paper was supported by the National 863 High Technology Develpoment Plan Project(Grant No.2001AA602015)
文摘The spectral methods and ice-induced fatigue analysis are discussed based on Miner＇s linear cumulative fatigue hypothesis and S-N curve data. According to the long-term data of full-scale tests on the platforms in the Bohai Sea, the ice force spectrum of conical structures and the fatigue environmental model are established. Moreover, the finite element model of JZ20-2MSW platform, an example of ice-induced fatigue analysis, is built with ANSYS software. The mode analysis and dynamic analysis in frequency domain under all kinds of ice fatigue work conditions are carded on, and the fatigue life of the structure is estimated in detail. The methods in this paper can be helpful in ice-induced fatigue analysis of ice-resistant platforms.
基金National Key Technology R & D Program-On-site Rapid Identification of Drug Research Project (Grant No. 2008BAI55B06)
文摘We analyzed the infrared 0R）-near infrared （NIR） 2D correlation spectra of drugs perturbed by temperature. By identification of functional groups by IR spectrum and by the correlation analysis of IR-NIR spectrum, we identified the characteristic spectral bands that were closely related to the structure of a drug substance of interest. These characteristic spectral bands were relatively less interfered by other ingredients for analysis by the NIR correlation coefficient method. With these characteristic spectral bands, the accuracy of screening illegally added Sildenafil citrate, Tadalafil and Metforrnin hydrochloride in Chinese patent drugs and healthcare products reached about 90%, which met the requirements of rapid screening.
基金This work was supported by the National Science Foundation of China(10271034)
文摘The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estimation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d（AN,A） → 0 are proved.
文摘This paper is confined to analyzing and implementing new spectral solutions of the fractional Riccati differential equation based on the application of the spectral tau method.A new explicit formula for approximating the fractional derivatives of shifted Chebyshev polynomials of the second kind in terms of their original polynomials is established.This formula is expressed in terms of a certain terminating hypergeometric function of the type_(4)F_(3)(1).This hypergeometric function is reduced in case of the integer case into a certain terminating hypergeometric function of the type 3 F 2(1)which can be summed with the aid of Watson’s identity.Six illustrative examples are presented to ensure the applicability and accuracy of the proposed algorithm.
基金supported by the State Key Program of National Natural Science Foundation of China(11931003)the National Natural Science Foundation of China(41974133,11671157)。
文摘In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51309050 and 51221961)the National Basic Research Program of China(973 Program,Grant Nos.2013CB036101 and 2011CB013703)
文摘In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.
基金National Natural Science Foundation of China under Grant No.51078337,No.51108431 and No.91315301
文摘The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.
