This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called...This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.展开更多
This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference m...This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.展开更多
First at all, it introduced the concept and the damages of continuous cropping obstacle. Then, it analyzed the causes of continuous cropping obstacles for Atractylodes macrocephala Koidz. In the end, in order to provi...First at all, it introduced the concept and the damages of continuous cropping obstacle. Then, it analyzed the causes of continuous cropping obstacles for Atractylodes macrocephala Koidz. In the end, in order to provide guidance for pro- moting sustainable development of Atractylodes macrocephala Koidz industry in Pingjiang County, it put forward some control methods for eliminating continuous cropping obstacles of Atractylodes macrocephala Koidz, including breeding varieties with high resistance; applying rotation cropping and intercropping reasonable; rational fertilization and soil disinfection; introducing antagonistic bacterial and eliminating au- tointoxication.展开更多
Non-pillar continuous mining(NPCM) is regarded as a high-efficient, high-level and one-step mining technology, which can be divided into two substopes. Back fill stability status in substope I, which directly influenc...Non-pillar continuous mining(NPCM) is regarded as a high-efficient, high-level and one-step mining technology, which can be divided into two substopes. Back fill stability status in substope I, which directly influence the loss rate and dilution rate, etc, will determine whether the experimental research is successful or not. By employing energy method of limit analysis and finite element numerical simulation method, the critical backfill height was determined under the prerequisite condition of its stability, which put forward theoretical basis for reasonable and correct selection of backfill’s parameters. The result showed that the first backfill could not keep stable for NPCM, while the other was able to.展开更多
Deformation behavior of slab at the straightening stage during continuous casting was simulated by the explicit dynamic finite element method,and the stress distribution along the width direction of the slab and its c...Deformation behavior of slab at the straightening stage during continuous casting was simulated by the explicit dynamic finite element method,and the stress distribution along the width direction of the slab and its change regularity at slab center during continuous casting were obtained.The influence of distribution and change of stress on the propagation of longitudinal cracks on slab surface was discussed.The results show that the tensional stress appears on slab surface at the inner arc side and the compressive stress appears on slab surface at the outer arc side at stages 6-8 in straightening zone during continuous casting.Longitudinal cracks generally appear on slab top surface and do not appear on slab bottom surface,which are also observed in industry.展开更多
In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopt...In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method （FVM）. Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.展开更多
On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these meth...On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.展开更多
The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze th...The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.展开更多
A new algorithm is presented by using the ant colony algorithm based on genetic method （ACG） to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of componen...A new algorithm is presented by using the ant colony algorithm based on genetic method （ACG） to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of component, trail information and fitness. The ant chooses a seed from the seed set with the possibility determined by trail information and fitness of the seed. The genetic method is used to form new solutions from the solutions got by the ants. Best solutions are selected to update the seeds in the sets and trail information of the seeds. In updating the trail information, a diffusion function is used to achieve the diffuseness of trail information. The new algorithm is tested with 8 different benchmark functions.展开更多
Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the ...Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.展开更多
In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Dis...In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.展开更多
By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive...By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.展开更多
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved hav...By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.展开更多
We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the numb...We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems.展开更多
In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique pro...In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization of the variables, linearization or small perturbations. The results seem to show that the method is very reliable and convenient for solving such equations.展开更多
Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solve...Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.展开更多
It's common to use the method of continuous spectroscopy in water quality testing. But there're some problems with it. For example, the scanning results have a large number of nonlinear signals, and the covari...It's common to use the method of continuous spectroscopy in water quality testing. But there're some problems with it. For example, the scanning results have a large number of nonlinear signals, and the covariance between variables is serious, which can lead to a decrease in the model prediction accuracy. In this paper, the standard solutions of nitrate nitrogen(NO_(3)-N) and nitrite nitrogen(NO_(2)-N) were used as the subject to be tested, and the data of the scanned waves and absorbance were obtained by use of spectral detector. The data were processed by noise reduction first and then the random forest(RF) algorithm was adopted to establish the regression relationship between concentration and absorbance. For comparison, partial least squares(PLS) and support vector machine(SVM) algorithm models were also established. For the same given data, the three reverse models can make the projection of the concentration respectively. The experimental results show that the RF algorithm predicts NO_(2)-N concentrations significantly better than the SVM algorithm and PLS algorithm. This proves that the RF algorithm has good prediction ability in spectral water quality detection because of its high model accuracy and better adaptability, which could be a reference for similar research on continuous spectral water quality online detection.展开更多
This paper proposes a continuous block method for the solution of second order ordinary differential equation. Collocation and interpolation of the power series approximate solution are adopted to derive a continuous ...This paper proposes a continuous block method for the solution of second order ordinary differential equation. Collocation and interpolation of the power series approximate solution are adopted to derive a continuous implicit linear multistep method. Continuous block method is used to derive the independent solution which is evaluated at selected grid points to generate the discrete block method. The order, consistency, zero stability and stability region are investigated. The new method was found to compare favourably with the existing methods in term of accuracy.展开更多
A new method called mixed Lagrangian and Eulerian method （MILE method） was used to simulate the thermomechanical behavior during continuous casting process of steel YF45MnV. The simulation results are basically in a...A new method called mixed Lagrangian and Eulerian method （MILE method） was used to simulate the thermomechanical behavior during continuous casting process of steel YF45MnV. The simulation results are basically in agreement with the measured data. The delaying period at the beginning of solidification is about 0.1. in square root of solidification time which is agreement with the data in literatures, and shell thickness increases in linear relation to square root of solidification time. The bloom surface temperature decreases gradually as the casting proceeds. The effective stress in the comer is much larger than that in the mid-face. The comer area is the dangerous zone of cracking. The effects of mold flux break temperature on the air gap and hot tearing indicator were also modeled. The model predicts that the bloom surface temperature increases with the increase of the mold flux break temperature, but the heat flux decreases with the increase of the mold flux break temperature. ,The hot tearing indicator is much smaller when the mold flux break temperature is higher.展开更多
In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evalua...In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.展开更多
文摘This paper deals with the numerical solutions of two-dimensional(2D)semi-linear reaction-diffusion equations(SLRDEs)with piecewise continuous argument(PCA)in reaction term.A high-order compact difference method called Ⅰ-type basic scheme is developed for solving the equations and it is proved under the suitable conditions that this method has the computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4)),where τ,h_(x )and h_(y) are the calculation stepsizes of the method in t-,x-and y-direction,respectively.With the above method and Newton linearized technique,a Ⅱ-type basic scheme is also suggested.Based on the both basic schemes,the corresponding Ⅰ-and Ⅱ-type alternating direction implicit(ADI)schemes are derived.Finally,with a series of numerical experiments,the computational accuracy and efficiency of the four numerical schemes are further illustrated.
文摘This paper deals with numerical computation and analysis for the initial boundary problems of two dimensional(2D)Sobolev equations with piecewise continuous argument.Firstly,a two-level high-order compact difference method(HOCDM)with computational accuracy O(τ^(2)+h_(x)^(4)+h_(y)^(4))is suggested,whereτ,h_(x),h_(y) denote the temporal and spatial stepsizes of the method,respectively.In order to improve the temporal computational accuracy of this method,the Richardson extrapolation technique is used and thus a new two-level HOCDMis derived,which is proved to be convergent of order four both in time and space.Although the new two-level HOCDM has the higher computational accuracy in time than the previous one,it will bring a larger computational cost.To overcome this deficiency,a three-level HOCDM with computational accuracy O(τ^(4)+h_(x)^(4)+h_(y)^(4))is constructed.Finally,with a series of numerical experiments,the theoretical accuracy and computational efficiency of the above methods are further verified.
文摘First at all, it introduced the concept and the damages of continuous cropping obstacle. Then, it analyzed the causes of continuous cropping obstacles for Atractylodes macrocephala Koidz. In the end, in order to provide guidance for pro- moting sustainable development of Atractylodes macrocephala Koidz industry in Pingjiang County, it put forward some control methods for eliminating continuous cropping obstacles of Atractylodes macrocephala Koidz, including breeding varieties with high resistance; applying rotation cropping and intercropping reasonable; rational fertilization and soil disinfection; introducing antagonistic bacterial and eliminating au- tointoxication.
文摘Non-pillar continuous mining(NPCM) is regarded as a high-efficient, high-level and one-step mining technology, which can be divided into two substopes. Back fill stability status in substope I, which directly influence the loss rate and dilution rate, etc, will determine whether the experimental research is successful or not. By employing energy method of limit analysis and finite element numerical simulation method, the critical backfill height was determined under the prerequisite condition of its stability, which put forward theoretical basis for reasonable and correct selection of backfill’s parameters. The result showed that the first backfill could not keep stable for NPCM, while the other was able to.
基金Project(50634030) supported by the National Natural Science Foundation of ChinaProject(20090042120005) supported by the Doctorate Foundation of the Ministry of Education of ChinaProject(2006CB605208-1) supported by the State Basic Research Program of China
文摘Deformation behavior of slab at the straightening stage during continuous casting was simulated by the explicit dynamic finite element method,and the stress distribution along the width direction of the slab and its change regularity at slab center during continuous casting were obtained.The influence of distribution and change of stress on the propagation of longitudinal cracks on slab surface was discussed.The results show that the tensional stress appears on slab surface at the inner arc side and the compressive stress appears on slab surface at the outer arc side at stages 6-8 in straightening zone during continuous casting.Longitudinal cracks generally appear on slab top surface and do not appear on slab bottom surface,which are also observed in industry.
基金supported by the Shanghai Municipal Natural Science Foundation(No.13ZR1415700)
文摘In this paper, a new unsteady aerodynamic design method is presented based on the Navier-Stokes equations and a continuous adjoint approach. A basic framework of time-accurate unsteady airfoil optimization which adopts time-averaged aerodynamic coefficients as objective functions is presented. The time-accurate continuous adjoint equation and its boundary conditions are derived. The flow field and the adjoint equation are simulated numerically by the finite volume method （FVM）. Feasibility and accuracy of the approach are perfectly validated by the design optimization results of the plunging NACA0012 airfoil.
基金supported by NSFC(11571266,91430106,11171168,11071132)NSFC-RGC(China-Hong Kong)(11661161017)
文摘On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming （bi）linear macroelements or （bi）quadratic elements, and the rotation by conforming （bi）linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.
文摘The particle path tracking method is proposed and used in two-dimensional（2D） and three-dimensional（3D） numerical simulations of continuously rotating detonation engines（CRDEs）. This method is used to analyze the combustion and expansion processes of the fresh particles, and the thermodynamic cycle process of CRDE. In a 3D CRDE flow field, as the radius of the annulus increases, the no-injection area proportion increases, the non-detonation proportion decreases, and the detonation height decreases. The flow field parameters on the 3D mid annulus are different from in the 2D flow field under the same chamber size. The non-detonation proportion in the 3D flow field is less than in the 2D flow field. In the 2D and 3D CRDE, the paths of the flow particles have only a small fluctuation in the circumferential direction. The numerical thermodynamic cycle processes are qualitatively consistent with the three ideal cycle models, and they are right in between the ideal F–J cycle and ideal ZND cycle. The net mechanical work and thermal efficiency are slightly smaller in the 2D simulation than in the 3D simulation. In the 3D CRDE, as the radius of the annulus increases, the net mechanical work is almost constant, and the thermal efficiency increases. The numerical thermal efficiencies are larger than F–J cycle, and much smaller than ZND cycle.
基金project supported by the National High-Technology Research and Development Program of China(Grant No.8632005AA642010)
文摘A new algorithm is presented by using the ant colony algorithm based on genetic method （ACG） to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of component, trail information and fitness. The ant chooses a seed from the seed set with the possibility determined by trail information and fitness of the seed. The genetic method is used to form new solutions from the solutions got by the ants. Best solutions are selected to update the seeds in the sets and trail information of the seeds. In updating the trail information, a diffusion function is used to achieve the diffuseness of trail information. The new algorithm is tested with 8 different benchmark functions.
基金This work was supported by the National Natural Science Foundation of China(11872080)Beijing Natural Science Foundation(3192005).
文摘Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.
文摘In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.
文摘By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.
基金Project supported by the National Natural Science Foundation of China (No.10471038)
文摘By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agree-ment with theory.
文摘We propose a continuous analogy of Newton’s method with inner iteration for solving a system of linear algebraic equations. Implementation of inner iterations is carried out in two ways. The former is to fix the number of inner iterations in advance. The latter is to use the inexact Newton method for solution of the linear system of equations that arises at each stage of outer iterations. We give some new choices of iteration parameter and of forcing term, that ensure the convergence of iterations. The performance and efficiency of the proposed iteration is illustrated by numerical examples that represent a wide range of typical systems.
文摘In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization of the variables, linearization or small perturbations. The results seem to show that the method is very reliable and convenient for solving such equations.
文摘Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions.These methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments.Discontinuous Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the convergence.Here we propose the use of FC in forming a new basis for the DG framework.
基金supported by the National Natural Science Foundation of China (No.51205005)the Beijing Science and Technology Innovation Service Ability Building (No.PXM2017-014212-000013)。
文摘It's common to use the method of continuous spectroscopy in water quality testing. But there're some problems with it. For example, the scanning results have a large number of nonlinear signals, and the covariance between variables is serious, which can lead to a decrease in the model prediction accuracy. In this paper, the standard solutions of nitrate nitrogen(NO_(3)-N) and nitrite nitrogen(NO_(2)-N) were used as the subject to be tested, and the data of the scanned waves and absorbance were obtained by use of spectral detector. The data were processed by noise reduction first and then the random forest(RF) algorithm was adopted to establish the regression relationship between concentration and absorbance. For comparison, partial least squares(PLS) and support vector machine(SVM) algorithm models were also established. For the same given data, the three reverse models can make the projection of the concentration respectively. The experimental results show that the RF algorithm predicts NO_(2)-N concentrations significantly better than the SVM algorithm and PLS algorithm. This proves that the RF algorithm has good prediction ability in spectral water quality detection because of its high model accuracy and better adaptability, which could be a reference for similar research on continuous spectral water quality online detection.
文摘This paper proposes a continuous block method for the solution of second order ordinary differential equation. Collocation and interpolation of the power series approximate solution are adopted to derive a continuous implicit linear multistep method. Continuous block method is used to derive the independent solution which is evaluated at selected grid points to generate the discrete block method. The order, consistency, zero stability and stability region are investigated. The new method was found to compare favourably with the existing methods in term of accuracy.
基金Project(51174020) supported by the National Natural Science Foundation of China
文摘A new method called mixed Lagrangian and Eulerian method （MILE method） was used to simulate the thermomechanical behavior during continuous casting process of steel YF45MnV. The simulation results are basically in agreement with the measured data. The delaying period at the beginning of solidification is about 0.1. in square root of solidification time which is agreement with the data in literatures, and shell thickness increases in linear relation to square root of solidification time. The bloom surface temperature decreases gradually as the casting proceeds. The effective stress in the comer is much larger than that in the mid-face. The comer area is the dangerous zone of cracking. The effects of mold flux break temperature on the air gap and hot tearing indicator were also modeled. The model predicts that the bloom surface temperature increases with the increase of the mold flux break temperature, but the heat flux decreases with the increase of the mold flux break temperature. ,The hot tearing indicator is much smaller when the mold flux break temperature is higher.
文摘In this paper, we developed a new continuous block method by the method of interpolation and collocation to derive new scheme. We adopted the use of power series as a basis function for approximate solution. We evaluated at off grid points to get a continuous hybrid multistep method. The continuous hybrid multistep method is solved for the independent solution to yield a continuous block method which is evaluated at selected points to yield a discrete block method. The basic properties of the block method were investigated and found to be consistent, zero stable and convergent. The results were found to compete favorably with the existing methods in terms of accuracy and error bound. In particular, the scheme was found to have a large region of absolute stability. The new method was tested on real life problem namely: Dynamic model.
