Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of thes...Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of these missing data is highly valuable for engineering and scientific research.In this study,the radial basis function(RBF)method is used to estimate the spatial distribution of total suspended matter(TSM)concentration in Hangzhou Bay using remote sensing data with severe data gaps.The estimation precision is validated by comparing the results with those of other commonly used interpolation methods,such as the Kriging method and the basic spline(B-spline)method.In addition,the applicability of the RBF method is explored.Results show that the estimation of the RBF method is significantly close to the observation in Hangzhou Bay.The average of the mean absolute error,mean relative error,and root mean square error in all the experiments is evidently smaller than those of the Kriging and B-spline interpolations,indicating that the proposed method is more appropriate for estimating the spatial distribution of the TSM in Hangzhou Bay.Finally,the TSM distribution in the blank observational area is predicted.This study can provide some reference values for handling watercolor remote sensing data.展开更多
To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The R...To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The RBM,constructed via eigenvector continuation and trained on both bound and resonant configurations,enables the fast and accurate emulation of resonance properties across the parameter space.To identify the physical resonant states from the emulator’s output,we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts.By applying this framework to unbound nucleus ^(6)Be,we quantified the model uncertainty in the predicted complex energies.The results demonstrate relative errors of 17.48%in the real part and 8.24%in the imaginary part,while achieving a speedup of four orders of magnitude compared with the full GCC calculations.To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework,we employed a Lippmann–Schwinger(L–S)-based correction scheme.This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane.By bridging the gap between bound-state and continuum regimes,the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.展开更多
We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground...We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.展开更多
The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and ...The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.展开更多
The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering ...The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to il-lustrate the computational accuracy and efficiency of the proposed method.展开更多
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable ...A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.展开更多
A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. ...A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.展开更多
It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method wide...It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.展开更多
Strong form collocation with radial basis approximation is introduced for the numerical solution of transient dynamics.Von Neumann stability analysis of this radial basis collocation method is performed to obtain the ...Strong form collocation with radial basis approximation is introduced for the numerical solution of transient dynamics.Von Neumann stability analysis of this radial basis collocation method is performed to obtain the stability conditions for second order wave equation with central difference temporal discretization.The shape parameter of the radial basis functions not only has strong influence on the spatial stability and accuracy,but also has profound influence on the temporal stability.Numerical studies are conducted and show reasonable agreement with stability analysis.Conclusions of selecting shape parameters as well as spatial discretization for solution stability are also presented.展开更多
Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order...Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.展开更多
The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode su...The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.展开更多
A new partial pricing column rule is proposed to the basis-deficiency-allowing simplex method developed by Pan.Computational results obtained with a set of small problems and a set of standard NETLIB problems show its...A new partial pricing column rule is proposed to the basis-deficiency-allowing simplex method developed by Pan.Computational results obtained with a set of small problems and a set of standard NETLIB problems show its promise of success.展开更多
The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the convent...The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the conventional MLCBFM based on Foldy-Lax multiple scattering equations,the improvement is only made in the generation of characteristic basis functions(CBFs).However,it does not provide a change in impedance matrix filling and reducing matrix calculation procedure,which is time-consuming.In reality,all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently.Therefore,ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study.Numerical results are given to demonstrate the accuracy and efficiency of the method.展开更多
Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years,owing to their practical significance and numerous applications in astro-physical and geo-physical phenomena.In...Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years,owing to their practical significance and numerous applications in astro-physical and geo-physical phenomena.In this paper,the radial base function was utilized to answer fractional equation associated with fluid flow passing through two parallel flat plates with a magnetic field.The magnetohydrodynamics coupled stress fluid flows between two parallel plates,with the bottom plate being stationary and the top plate moving at a persistent velocity.We compared the radial basis function approach to the numerical method(fourth-order Range-Kutta)in order to verify its validity.The findings demonstrated that the discrepancy between these two techniques is quite negligible,indicating that this method is very reliable.The impact of the magnetic field parameter and Reynolds number on the velocity distribution perpendicular to the fluid flow direction is illustrated.Eventually,the velocity parameter is compared for diverse conditionsα,Reynolds and position(y),the maximum of which occurs atα=0.4.Also,the maximum velocity values occur inα=0.4 and Re=1000 and the concavity of the graph is less forα=0.8.展开更多
This study aimed to optimize the rapid test factors of dry basis weight of reconstituted tobacco, in order to afford a reference test method for companies which produce reconstituted tobacco to better control the basi...This study aimed to optimize the rapid test factors of dry basis weight of reconstituted tobacco, in order to afford a reference test method for companies which produce reconstituted tobacco to better control the basis weight and coating ratio on line. The dry basis weight of reconstituted tobacco was tested by fast method and normal oven method individually. And the effects on the test values of different test factors such as temperature, time and the number of baking sheets were studied. Then the test values of these two methods were compared, so the proper factors of rapid test method were determined. As the baking temperature rose from 130 ℃ to 150 ℃, and the baking time rose from 1 min to 2 min, the difference between fast test method and normal oven method grew, and when the number of baking pieces rose from 3 pieces to 5 pieces, the difference between the two methods went down. The optimum test condition was baking temperature of 130 ℃, baking time of 1 min, and baking sample sheet number of 5. Under this condition, the value of fast test method was the closest to the test value of normal oven method, and meanwhile, the test factor was more proper for testing on line. The study will provide a reference for online controlling of dry basis weight and coating ratio of reconstituted tobacco.展开更多
Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the b...Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.展开更多
In this paper,we develop novel local discontinuous Galerkin(LDG)methods for fractional diffusion equations with non-smooth solutions.We consider such problems,for which the solutions are not smooth at boundary,and the...In this paper,we develop novel local discontinuous Galerkin(LDG)methods for fractional diffusion equations with non-smooth solutions.We consider such problems,for which the solutions are not smooth at boundary,and therefore the traditional LDG methods with piecewise polynomial solutions suffer accuracy degeneracy.The novel LDG methods utilize a solution information enriched basis,simulate the problem on a paired special mesh,and achieve optimal order of accuracy.We analyze the L2 stability and optimal error estimate in L2-norm.Finally,numerical examples are presented for validating the theoretical conclusions.展开更多
Characteristic Basis Function Method (CBFM) is a novel approach for analyzing the ElectroMagnetic (EM) scattering from electrically large objects. Based on dividing the studied object into small blocks, the CBFM is su...Characteristic Basis Function Method (CBFM) is a novel approach for analyzing the ElectroMagnetic (EM) scattering from electrically large objects. Based on dividing the studied object into small blocks, the CBFM is suitable for parallel computing. In this paper, a static load balance parallel method is presented by combining Message Passing Interface (MPI) with Adaptively Modified CBFM (AMCBFM). In this method, the object geometry is partitioned into distinct blocks, and the serial number of blocks is sent to related nodes according to a certain rule. Every node only needs to calculate the information on local blocks. The obtained results confirm the accuracy and efficiency of the proposed method in speeding up solving large electrical scale problems.展开更多
基金supported by the Open Funds for Hubei Key Laboratory of Marine Geological Resources,China University of Geosciences(No.MGR202308)the Natural Science Foundation of Shandong Province(No.ZR2020MD085)+3 种基金the National Natural Science Foundation of China(No.41821004)the Taishan Scholar Program(No.tstp2022114)the Shandong Provincial Natural Science Foundation(No.DKXZZ202206)the National Key Research and Development Program of China(No.2016YFC1402404).
文摘Ocean remote sensing satellites provide observations with high spatiotemporal resolution.However,the influence of clouds,fog,and haze frequently leads to significant data gaps.Accurate and effective estimation of these missing data is highly valuable for engineering and scientific research.In this study,the radial basis function(RBF)method is used to estimate the spatial distribution of total suspended matter(TSM)concentration in Hangzhou Bay using remote sensing data with severe data gaps.The estimation precision is validated by comparing the results with those of other commonly used interpolation methods,such as the Kriging method and the basic spline(B-spline)method.In addition,the applicability of the RBF method is explored.Results show that the estimation of the RBF method is significantly close to the observation in Hangzhou Bay.The average of the mean absolute error,mean relative error,and root mean square error in all the experiments is evidently smaller than those of the Kriging and B-spline interpolations,indicating that the proposed method is more appropriate for estimating the spatial distribution of the TSM in Hangzhou Bay.Finally,the TSM distribution in the blank observational area is predicted.This study can provide some reference values for handling watercolor remote sensing data.
基金supported by the National Key Research and Development Program(MOST 2023YFA1606404 and MOST 2022YFA1602303)the National Natural Science Foundation of China(Nos.12347106,12147101,and 12447122)the China Postdoctoral Science Foundation(No.2024M760489).
文摘To study the uncertainty quantification of resonant states in open quantum systems,we developed a Bayesian framework by integrating a reduced basis method(RBM)emulator with the Gamow coupled-channel(GCC)approach.The RBM,constructed via eigenvector continuation and trained on both bound and resonant configurations,enables the fast and accurate emulation of resonance properties across the parameter space.To identify the physical resonant states from the emulator’s output,we introduce an overlap-based selection technique that effectively isolates true solutions from background artifacts.By applying this framework to unbound nucleus ^(6)Be,we quantified the model uncertainty in the predicted complex energies.The results demonstrate relative errors of 17.48%in the real part and 8.24%in the imaginary part,while achieving a speedup of four orders of magnitude compared with the full GCC calculations.To further investigate the asymptotic behavior of the resonant-state wavefunctions within the RBM framework,we employed a Lippmann–Schwinger(L–S)-based correction scheme.This approach not only improves the consistency between eigenvalues and wavefunctions but also enables a seamless extension from real-space training data to the complex energy plane.By bridging the gap between bound-state and continuum regimes,the L–S correction significantly enhances the emulator’s capability to accurately capture continuum structures in open quantum systems.
基金supported by the National Key R&D Program of China(No.2023YFA1606701)the National Natural Science Foundation of China(Nos.12175042,11890710,11890714,12047514,12147101,and 12347106)+1 种基金Guangdong Major Project of Basic and Applied Basic Research(No.2020B0301030008)China National Key R&D Program(No.2022YFA1602402).
文摘We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions.
文摘The present work describes the application of the method of fundamental solutions （MFS） along with the analog equation method （AEM） and radial basis function （RBF） approximation for solving the 2D isotropic and anisotropic Helmholtz problems with different wave numbers. The AEM is used to convert the original governing equation into the classical Poisson＇s equation, and the MFS and RBF approximations are used to derive the homogeneous and particular solutions, respectively. Finally, the satisfaction of the solution consisting of the homogeneous and particular parts to the related governing equation and boundary conditions can produce a system of linear equations, which can be solved with the singular value decomposition （SVD） technique. In the computation, such crucial factors related to the MFS-RBF as the location of the virtual boundary, the differential and integrating strategies, and the variation of shape parameters in multi-quadric （MQ） are fully analyzed to provide useful reference.
基金Supported by the National Natural Science Foundation of China (No. 60771034 )the 211 Project of Anhui University
文摘The Asymptotic Waveform Evaluation (AWE) technique is an extrapolation method that provides a reduced-order model of linear system and has already been successfully used to analyze wideband electromagnetic scattering problems. As the number of unknowns increases, the size of Method Of Moments (MOM) impedance matrix grows very rapidly, so it is a prohibitive task for the computation of wideband Radar Cross Section (RCS) from electrically large object or multi-objects using the traditional AWE technique that needs to solve directly matrix inversion. In this paper, an AWE technique based on the Characteristic Basis Function (CBF) method, which can reduce the matrix size to a manageable size for direct matrix inversion, is proposed to analyze electromagnetic scattering from multi-objects over a given frequency band. Numerical examples are presented to il-lustrate the computational accuracy and efficiency of the proposed method.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
文摘A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.
文摘A non-orthogonal predefined exponential basis set is used to handle half-bounded domains in multi domain spectral method (MDSM). This approach works extremely well for real-valued semi-infinite differential problems. It spans simultaneously wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to solve different problems and compared with analytical and published results. The comparison exhibits the strengths and accuracy of the presented basis set.
基金provided by China Geological Survey with the project(Nos.DD20190707,DD20190012)the Fundamental Research Funds for China Central public research Institutes with the project(No.JKY202014)
文摘It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.
文摘Strong form collocation with radial basis approximation is introduced for the numerical solution of transient dynamics.Von Neumann stability analysis of this radial basis collocation method is performed to obtain the stability conditions for second order wave equation with central difference temporal discretization.The shape parameter of the radial basis functions not only has strong influence on the spatial stability and accuracy,but also has profound influence on the temporal stability.Numerical studies are conducted and show reasonable agreement with stability analysis.Conclusions of selecting shape parameters as well as spatial discretization for solution stability are also presented.
文摘Recently many research works have been conducted and published regarding fractional order differential equations. There are several approaches available for numerical approximations of the solution of fractional order diffusion equations. Spectral collocation method based on Lagrange’s basis polynomials to approximate numerical solutions of one-dimensional (1D) space fractional diffusion equations are introduced in this research paper. The proposed form of approximate solution satisfies non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme produce a system of first order Ordinary Differential Equations (ODE) from the fractional diffusion equation. We applied this method with four different sets of collocation points to compare their performance.
文摘The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.
基金This work is supported by the NSF of China,No.10371017NSF Grant of Hangzhou Dianzi University KYS091504025.
文摘A new partial pricing column rule is proposed to the basis-deficiency-allowing simplex method developed by Pan.Computational results obtained with a set of small problems and a set of standard NETLIB problems show its promise of success.
基金supported by the National Natural Science Foundation of China (No.61401003)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No.20123401110006)the Natural Science Research Project of Anhui Education ( No. KJ2015A436)
文摘The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the conventional MLCBFM based on Foldy-Lax multiple scattering equations,the improvement is only made in the generation of characteristic basis functions(CBFs).However,it does not provide a change in impedance matrix filling and reducing matrix calculation procedure,which is time-consuming.In reality,all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently.Therefore,ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study.Numerical results are given to demonstrate the accuracy and efficiency of the method.
文摘Investigations into the magnetohydrodynamics of viscous fluids have become more important in recent years,owing to their practical significance and numerous applications in astro-physical and geo-physical phenomena.In this paper,the radial base function was utilized to answer fractional equation associated with fluid flow passing through two parallel flat plates with a magnetic field.The magnetohydrodynamics coupled stress fluid flows between two parallel plates,with the bottom plate being stationary and the top plate moving at a persistent velocity.We compared the radial basis function approach to the numerical method(fourth-order Range-Kutta)in order to verify its validity.The findings demonstrated that the discrepancy between these two techniques is quite negligible,indicating that this method is very reliable.The impact of the magnetic field parameter and Reynolds number on the velocity distribution perpendicular to the fluid flow direction is illustrated.Eventually,the velocity parameter is compared for diverse conditionsα,Reynolds and position(y),the maximum of which occurs atα=0.4.Also,the maximum velocity values occur inα=0.4 and Re=1000 and the concavity of the graph is less forα=0.8.
基金Supported by Science and Technology Planning Project of China Tobacco Schweitzer(Yunnan)Reconstituted Tobacco Co.,Ltd.(KY-17-ZL-01)China Tobacco Yunnan Industrial Co.,Ltd.(2016YL02)
文摘This study aimed to optimize the rapid test factors of dry basis weight of reconstituted tobacco, in order to afford a reference test method for companies which produce reconstituted tobacco to better control the basis weight and coating ratio on line. The dry basis weight of reconstituted tobacco was tested by fast method and normal oven method individually. And the effects on the test values of different test factors such as temperature, time and the number of baking sheets were studied. Then the test values of these two methods were compared, so the proper factors of rapid test method were determined. As the baking temperature rose from 130 ℃ to 150 ℃, and the baking time rose from 1 min to 2 min, the difference between fast test method and normal oven method grew, and when the number of baking pieces rose from 3 pieces to 5 pieces, the difference between the two methods went down. The optimum test condition was baking temperature of 130 ℃, baking time of 1 min, and baking sample sheet number of 5. Under this condition, the value of fast test method was the closest to the test value of normal oven method, and meanwhile, the test factor was more proper for testing on line. The study will provide a reference for online controlling of dry basis weight and coating ratio of reconstituted tobacco.
文摘Background:This article investigates the Least-Squares Monte Carlo Method by using different polynomial basis in American Asian Options pricing.The standard approach in the option pricing literature is to choose the basis arbitrarily.By comparing four different polynomial basis we show that the choice of basis interferes in the option's price.Methods:We assess Least-Squares Method performance in pricing four different American Asian Options by using four polynomial basis:Power,Laguerre,Legendre and Hermite A.To every American Asian Option priced,three sets of parameters are used in order to evaluate it properly.Results:We show that the choice of the basis interferes in the option's price by showing that one of them converges to the option's value faster than any other by using fewer simulated paths.In the case of an Amerasian call option,for example,we find that the preferable polynomial basis is Hermite A.For an Amerasian put option,the Power polynomial basis is recommended.Such empirical outcome is theoretically unpredictable,since in principle all basis can be indistinctly used when pricing the derivative.Conclusion:In this article The Least-Squares Monte Carlo Method performance is assessed in pricing four different types of American Asian Options by using four different polynomial basis through three different sets of parameters.Our results suggest that one polynomial basis is best suited to perform the method when pricing an American Asian option.Theoretically all basis can be indistinctly used when pricing the derivative.However,our results does not confirm these.We find that when pricing an American Asian put option,Power A is better than the other basis we have studied here whereas when pricing an American Asian call,Hermite A is better.
文摘In this paper,we develop novel local discontinuous Galerkin(LDG)methods for fractional diffusion equations with non-smooth solutions.We consider such problems,for which the solutions are not smooth at boundary,and therefore the traditional LDG methods with piecewise polynomial solutions suffer accuracy degeneracy.The novel LDG methods utilize a solution information enriched basis,simulate the problem on a paired special mesh,and achieve optimal order of accuracy.We analyze the L2 stability and optimal error estimate in L2-norm.Finally,numerical examples are presented for validating the theoretical conclusions.
文摘Characteristic Basis Function Method (CBFM) is a novel approach for analyzing the ElectroMagnetic (EM) scattering from electrically large objects. Based on dividing the studied object into small blocks, the CBFM is suitable for parallel computing. In this paper, a static load balance parallel method is presented by combining Message Passing Interface (MPI) with Adaptively Modified CBFM (AMCBFM). In this method, the object geometry is partitioned into distinct blocks, and the serial number of blocks is sent to related nodes according to a certain rule. Every node only needs to calculate the information on local blocks. The obtained results confirm the accuracy and efficiency of the proposed method in speeding up solving large electrical scale problems.
