A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this wor...A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties,flowing uniformly at a velocity U.The analysis focuses on four distinct types of nanoparticles,i.e.,Al2O3,Ag,carbon nanotube(CNT),and graphene.Specifically,two of these particles exhibit a spherical shape,one possesses a cylindrical form,and the final type adopts a platelet morphology.The investigation delves into the pairing of these nanoparticles.The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid.The fin design,under the specified circumstances,gives rise to the derivation of a differential equation.The given equation is then transformed into a dimensionless form.Notably,the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features.To validate the credibility of this research,the results obtained in this study are systematically compared with the numerical simulations.The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.展开更多
A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equat...A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.展开更多
Based on the borehole strainmeter recordings immediately before the strong earthquakes （Ms〉7.5） during the period from 2001 to 2005 observed at the Taian observation station, Shandong Province, the authors make a s...Based on the borehole strainmeter recordings immediately before the strong earthquakes （Ms〉7.5） during the period from 2001 to 2005 observed at the Taian observation station, Shandong Province, the authors make a systematic and objective examination of the precursor waves of the quakes. The effects of Earth tides with periods larger than 128 min are eliminated through high-pass filtering; and atmospheric-pressure inferences are removed by linear regression. The 2-128 min signals are then separated into six frequency bands by employing the wavelet method. Results indicate that the wavelet method is capable of picking out information of weak variations in the signals. According to the characteristics of the ＇precursor waves＇ obtained from wavelet transformation, the method of overrun ratio analysis is put forward for examination. All the detailed components of the wavelets have been analyzed. For the time series of the overrun rate in all these components, statisitical calculation has been made for the slopes of fit curves, and mean values and standard deviations were obtained and positive-negative slope ratios were analyzed. The three statistical data show that ＇precursor waves＇ are not widely recorded by borehole strainmeter within 15 days before remote strong earthquakes.展开更多
Electric signals are acquired and analyzed in order to monitor the underwater arc welding process. Voltage break point and magnitude are extracted by detecting arc voltage singularity through the modulus maximum wavel...Electric signals are acquired and analyzed in order to monitor the underwater arc welding process. Voltage break point and magnitude are extracted by detecting arc voltage singularity through the modulus maximum wavelet （MMW） method. A novel threshold algorithm, which compromises the hard-threshold wavelet （HTW） and soft-threshold wavelet （STW） methods, is investigated to eliminate welding current noise. Finally, advantages over traditional wavelet methods are verified by both simulation and experimental results.展开更多
Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the re...Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.展开更多
A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a G...A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.展开更多
The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear b...The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.展开更多
The ship hull surface optimization based on the wave resistance is an important issue in the ship engineering industry. The wavelet method may provide a convenient tool for the surface hull optimization. As a prelimin...The ship hull surface optimization based on the wave resistance is an important issue in the ship engineering industry. The wavelet method may provide a convenient tool for the surface hull optimization. As a preliminary study, we use the wavelet method to optimize the hull surface based on the Michel wave resistance for a Wigley model in this paper. Firstly, we express the model＇s surface by the wavelet decomposition expressions and obtain a reconstructed surface and then validate its accuracy. Secondly, we rewrite the Michel wave resistance formula in the wavelet bases, resulting in a simple formula containing only the ship hull surface＇s wavelet coefficients. Thirdly, we take these wavelet coefficients as optimization variables, and analyze the main wave resistance distribution in terms of scales and locations, to reduce the number of optimization variables. Finally, we obtain the optimal hull surface of the Wigley model through genetic algorithms, reducing the wave resistance almost by a half. It is shown that the wavelet method may provide a new approach for the hull optimization.展开更多
The backward heat equation is a typical ill-posed problem. In this paper, we shall apply a dual least squares method connecting Shannon wavelet to the following equation Motivated by Reginska＇s work, we shall give ...The backward heat equation is a typical ill-posed problem. In this paper, we shall apply a dual least squares method connecting Shannon wavelet to the following equation Motivated by Reginska＇s work, we shall give two nonlinear approximate methods to regularize the approximate solutions for high-dimensional backward heat equation, and prove that our methods are convergent.展开更多
This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes(HS-SWCNTs)conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field.The analysis utilizes Eule...This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes(HS-SWCNTs)conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field.The analysis utilizes Euler-Bernoulli beam model,considering the variable cross section,and incorporating Eringen’s nonlocal theory to formulate the governing partial differential equation of motion.The instability domain of HS-SWCNTs is estimated using Galerkin’s approach.Numerical analysis is performed using the Haar wavelet method.The critical buckling load obtained in this study is compared with previous research to validate the proposed model.The results highlight the effectiveness of the proposed model in assessing the vibrational characteristics of a complex multi-physics system involving HS-SWCNTs.Dispersion graphs and tables are presented to visualize the numerical findings pertaining to various system parameters,including the nonlocal parameter,magnetic flux,Knudsen number,and viscous factor.展开更多
A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and vi...A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.展开更多
We analyze the radio light curve of 3C 273 at 15 GHz from 1963 to 2006 taken from the database of the literature,and find evidence of quasi-periodic activity.Using the wavelet analysis method to analyze these data,our...We analyze the radio light curve of 3C 273 at 15 GHz from 1963 to 2006 taken from the database of the literature,and find evidence of quasi-periodic activity.Using the wavelet analysis method to analyze these data,our results indicate that:(1) There is one main outburst period of P1=8.1±0.1 year in 3C 273.This period is in a good agreement with Ozernoi's analysis in optical bands.(2) Based on the possible periods,we expect the next burst in 2014 October.展开更多
In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibi...In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.展开更多
The adaptive wavelet collocation method （AWCM） is a variable grid technology for solving partial differential equations （PDEs） with high singularities. Based on interpolating wavelets, the AWCM adapts the grid so ...The adaptive wavelet collocation method （AWCM） is a variable grid technology for solving partial differential equations （PDEs） with high singularities. Based on interpolating wavelets, the AWCM adapts the grid so that a higher resolution is automatically attributed to domain regions with high singularities. Accuracy problems with the AWCM have been reported in the literature, and in this paper problems of efficiency with the AWCM are discussed in detail through a simple one-dimensional （1D） nonlinear advection equation whose analytic solution is easily obtained. A simple and efficient implementation of the AWCM is investigated. Through studying the maximum errors at the moment of frontogenesis of the 1D nonlinear advection equation with different initial values and a comparison with the finite difference method （FDM） on a uniform grid, the AWCM shows good potential for modeling the front efficiently. The AWCM is also applied to a two-dimensional （2D） unbalanced frontogenesis model in its first attempt at numerical simulation of a meteorological front. Some important characteristics about the model are revealed by the new scheme.展开更多
Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copie...Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties.展开更多
This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is...This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.展开更多
We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can...We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.展开更多
In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] a...In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.展开更多
This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving one-dimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical flu...This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving one-dimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple applicability for a variety of boundary conditions and able to effectively approximate the solution of PDEs with less storage space and execution. The results of a numerical experiment are provided to verify the efficiency of the designed new technique.展开更多
The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary diffe...The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.展开更多
文摘A distinguished category of operational fluids,known as hybrid nanofluids,occupies a prominent role among various fluid types owing to its superior heat transfer properties.By employing a dovetail fin profile,this work investigates the thermal reaction of a dynamic fin system to a hybrid nanofluid with shape-based properties,flowing uniformly at a velocity U.The analysis focuses on four distinct types of nanoparticles,i.e.,Al2O3,Ag,carbon nanotube(CNT),and graphene.Specifically,two of these particles exhibit a spherical shape,one possesses a cylindrical form,and the final type adopts a platelet morphology.The investigation delves into the pairing of these nanoparticles.The examination employs a combined approach to assess the constructional and thermal exchange characteristics of the hybrid nanofluid.The fin design,under the specified circumstances,gives rise to the derivation of a differential equation.The given equation is then transformed into a dimensionless form.Notably,the Hermite wavelet method is introduced for the first time to address the challenge posed by a moving fin submerged in a hybrid nanofluid with shape-dependent features.To validate the credibility of this research,the results obtained in this study are systematically compared with the numerical simulations.The examination discloses that the highest heat flux is achieved when combining nanoparticles with spherical and platelet shapes.
基金Project supported by the National Natural Science Foundation of China(Nos.11472119,11032006 and 11121202)the National Key Project of Magneto-Constrained Fusion Energy Development Program(No.2013GB110002)the Scientific and Technological Self-innovation Foundation of Huazhong Agricultural University(No.52902-0900206074)
文摘A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.
基金supported by National Natural Science Foundation of China (40374011)Joint Seismological Science Foundation of China (1040037)
文摘Based on the borehole strainmeter recordings immediately before the strong earthquakes （Ms〉7.5） during the period from 2001 to 2005 observed at the Taian observation station, Shandong Province, the authors make a systematic and objective examination of the precursor waves of the quakes. The effects of Earth tides with periods larger than 128 min are eliminated through high-pass filtering; and atmospheric-pressure inferences are removed by linear regression. The 2-128 min signals are then separated into six frequency bands by employing the wavelet method. Results indicate that the wavelet method is capable of picking out information of weak variations in the signals. According to the characteristics of the ＇precursor waves＇ obtained from wavelet transformation, the method of overrun ratio analysis is put forward for examination. All the detailed components of the wavelets have been analyzed. For the time series of the overrun rate in all these components, statisitical calculation has been made for the slopes of fit curves, and mean values and standard deviations were obtained and positive-negative slope ratios were analyzed. The three statistical data show that ＇precursor waves＇ are not widely recorded by borehole strainmeter within 15 days before remote strong earthquakes.
文摘Electric signals are acquired and analyzed in order to monitor the underwater arc welding process. Voltage break point and magnitude are extracted by detecting arc voltage singularity through the modulus maximum wavelet （MMW） method. A novel threshold algorithm, which compromises the hard-threshold wavelet （HTW） and soft-threshold wavelet （STW） methods, is investigated to eliminate welding current noise. Finally, advantages over traditional wavelet methods are verified by both simulation and experimental results.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.11461026,11361024,51378206 and 11661036)the Provincial Natural Science Foundation(Grant No.2017BAB201009)
文摘Wavelet method is often used in analyzing trend and period of time sequence. When using wavelet method one serious problem is different chosen wavelet basis and scale would lead to different results. Sometimes, the results vary greatly. To overcome this problem and to improve the accuracy and efficiency, a new method denoted by Natural-based Wavelet Method is introduced and extended. It can be proved that the proposed method in fact is a special class of discrete wavelet. At first, two numerical examples are designed to show the capacity of the novel method. Second, this method is applied to a precipitation series. According to wavelet analysis and short-range precipitation prediction, this precipitation exists a faintly increasing trend. Through the analysis, the studied precipitation has two major periods: 11 and 41 years. The results validate that the Natural-based Wavelet Method used in application of multi-complicated observed data is suitable. It is easy to write the source code of the proposed method. When new information appears, new information can be easily added into the original sequence, this is another advantage of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.11502103 and11421062)the Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ15115)
文摘A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.
基金Project supported by the Natural National Science Foundation of China(Grant Nos.51309040,51379033)the National Key Basic Research Development Program of China(973 Program,Grant No.2013CB036101)the Fundamental research fund for the Central Universities(Grant No.DMU3132015089)
文摘The ship hull surface optimization based on the wave resistance is an important issue in the ship engineering industry. The wavelet method may provide a convenient tool for the surface hull optimization. As a preliminary study, we use the wavelet method to optimize the hull surface based on the Michel wave resistance for a Wigley model in this paper. Firstly, we express the model＇s surface by the wavelet decomposition expressions and obtain a reconstructed surface and then validate its accuracy. Secondly, we rewrite the Michel wave resistance formula in the wavelet bases, resulting in a simple formula containing only the ship hull surface＇s wavelet coefficients. Thirdly, we take these wavelet coefficients as optimization variables, and analyze the main wave resistance distribution in terms of scales and locations, to reduce the number of optimization variables. Finally, we obtain the optimal hull surface of the Wigley model through genetic algorithms, reducing the wave resistance almost by a half. It is shown that the wavelet method may provide a new approach for the hull optimization.
基金Supported by Beijing Natural Science Foundation(Grant No.1092003)Beijing Educational Committee Foundation(Grant No.PHR201008022) National Natural Science Foundation of China(Grant No.11271038)1)Corresponding author
文摘The backward heat equation is a typical ill-posed problem. In this paper, we shall apply a dual least squares method connecting Shannon wavelet to the following equation Motivated by Reginska＇s work, we shall give two nonlinear approximate methods to regularize the approximate solutions for high-dimensional backward heat equation, and prove that our methods are convergent.
文摘This research explores the dynamic behaviour of horn-shaped single-walled carbon nanotubes(HS-SWCNTs)conveying viscous nanofluid with pulsating the influence of a longitudinal magnetic field.The analysis utilizes Euler-Bernoulli beam model,considering the variable cross section,and incorporating Eringen’s nonlocal theory to formulate the governing partial differential equation of motion.The instability domain of HS-SWCNTs is estimated using Galerkin’s approach.Numerical analysis is performed using the Haar wavelet method.The critical buckling load obtained in this study is compared with previous research to validate the proposed model.The results highlight the effectiveness of the proposed model in assessing the vibrational characteristics of a complex multi-physics system involving HS-SWCNTs.Dispersion graphs and tables are presented to visualize the numerical findings pertaining to various system parameters,including the nonlocal parameter,magnetic flux,Knudsen number,and viscous factor.
基金This work was supported by the National Natural Science Foundation of China(Nos.51405370&51421004)the National Key Basic Research Program of China(No.2015CB057400)+2 种基金the project supported by Natural Science Basic Plan in Shaanxi Province of China(No.2015JQ5184)the Fundamental Research Funds for the Central Universities(xjj2014014)Shaanxi Province Postdoctoral Research Project.
文摘A new wavelet finite element method(WFEM)is constructed in this paper and two elements for bending and free vibration problems of a stiffened plate are analyzed.By means of generalized potential energy function and virtual work principle,the formulations of the bending and free vibration problems of the stiffened plate are derived separately.Then,the scaling functions of the B-spline wavelet on the interval(BSWI)are introduced to discrete the solving field variables instead of conventional polynomial interpolation.Finally,the corresponding two problems can be resolved following the traditional finite element frame.There are some advantages of the constructed elements in structural analysis.Due to the excellent features of the wavelet,such as multi-scale and localization characteristics,and the excellent numerical approximation property of the BSWI,the precise and efficient analysis can be achieved.Besides,transformation matrix is used to translate the meaningless wavelet coefficients into physical space,thus the resolving process is simplified.In order to verify the superiority of the constructed method in stiffened plate analysis,several numerical examples are given in the end.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10821061,10763002,and 10663002)the National Basic Research Program of China (Grant No. 2009CB824800)
文摘We analyze the radio light curve of 3C 273 at 15 GHz from 1963 to 2006 taken from the database of the literature,and find evidence of quasi-periodic activity.Using the wavelet analysis method to analyze these data,our results indicate that:(1) There is one main outburst period of P1=8.1±0.1 year in 3C 273.This period is in a good agreement with Ozernoi's analysis in optical bands.(2) Based on the possible periods,we expect the next burst in 2014 October.
基金the National Natural Science Foundation of China(No.40774056)Program of Excellent Team in Harbin Institute of Technology
文摘In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.
基金supported by China Special Foundation for Public Service(Meteorology,GYHY200706033)Nature Science Foundation of China(Grant No.40675024)the State Key Basic Research Program(Grant No.2004CB18301)
文摘The adaptive wavelet collocation method （AWCM） is a variable grid technology for solving partial differential equations （PDEs） with high singularities. Based on interpolating wavelets, the AWCM adapts the grid so that a higher resolution is automatically attributed to domain regions with high singularities. Accuracy problems with the AWCM have been reported in the literature, and in this paper problems of efficiency with the AWCM are discussed in detail through a simple one-dimensional （1D） nonlinear advection equation whose analytic solution is easily obtained. A simple and efficient implementation of the AWCM is investigated. Through studying the maximum errors at the moment of frontogenesis of the 1D nonlinear advection equation with different initial values and a comparison with the finite difference method （FDM） on a uniform grid, the AWCM shows good potential for modeling the front efficiently. The AWCM is also applied to a two-dimensional （2D） unbalanced frontogenesis model in its first attempt at numerical simulation of a meteorological front. Some important characteristics about the model are revealed by the new scheme.
文摘Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties.
基金supported by the Program of Excellent Team of Harbin Institute of Technology
文摘This paper is concerned with estimation of electrical conductivity in Maxwell equations. The primary difficulty lies in the presence of numerous local minima in the objective functional. A wavelet multiscale method is introduced and applied to the inversion of Maxwell equations. The inverse problem is decomposed into multiple scales with wavelet transform, and hence the original problem is reformulated to a set of sub-inverse problems corresponding to different scales, which can be solved successively according to the size of scale from the shortest to the longest. The stable and fast regularized Gauss-Newton method is applied to each scale. Numerical results show that the proposed method is effective, especially in terms of wide convergence, computational efficiency and precision.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10971226,91130013,and 11001270)the National Basic Research Program of China(Grant No.2009CB723802)+1 种基金the Research Innovation Fund of Hunan Province,China (Grant No.CX2011B011)the Innovation Fund of National University of Defense Technology,China(Grant No.B120205)
文摘We propose a multi-symplectic wavelet splitting equations. Based on its mu]ti-symplectic formulation, method to solve the strongly coupled nonlinear SchrSdinger the strongly coupled nonlinear SchrSdinger equations can be split into one linear multi-symplectic subsystem and one nonlinear infinite-dimensional Hamiltonian subsystem. For the linear subsystem, the multi-symplectic wavelet collocation method and the symplectic Euler method are employed in spatial and temporal discretization, respectively. For the nonlinear subsystem, the mid-point symplectic scheme is used. Numerical simulations show the effectiveness of the proposed method during long-time numerical calculation.
文摘In this paper, we suggest a method for solving Fredholm integral equation of the first kind based on wavelet basis. The continuous Legendre and Chebyshev wavelets of the first, second, third and fourth kind on [0,1] are used and are utilized as a basis in Galerkin method to approximate the solution of integral equations. Then, in some examples the mentioned wavelets are compared with each other.
文摘This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving one-dimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple applicability for a variety of boundary conditions and able to effectively approximate the solution of PDEs with less storage space and execution. The results of a numerical experiment are provided to verify the efficiency of the designed new technique.
文摘The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.
