A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots ...A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.展开更多
Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution a...Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.展开更多
Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coeff...Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.展开更多
The magnetoresistance effect of a p-n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier...The magnetoresistance effect of a p-n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier generation- recombination model are introduced into a drift-diffusion transport model and carrier continuity equations. All the equa- tions are discretized by the finite-difference method and the box integration method and then solved by Newton iteration. Taking advantage of those models and methods, an abrupt junction with uniform doping is studied systematically, and the magnetoresistance as a function of doping concentration, SiO2 thickness and geometrical size is also investigated. The simulation results show that the magnetoresistance （MR） can be controlled substantially by the gate and is dependent on the polarity of the magnetic field.展开更多
Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by ...Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton＇s iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.展开更多
基金Foundation item： Supported by the National Science Foundation of China（10701066） Supported by the National Foundation of the Education Department of Henan Province（2008A110022）
文摘A fourth-order convergence method of solving roots for nonlinear equation, which is a variant of Newton＇s method given. Its convergence properties is proved. It is at least fourth-order convergence near simple roots and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton and Newton-type methods. The results show that the proposed method has some more advantages than others. It enriches the methods to find the roots of non-linear equations and it is important in both theory and application.
基金The authors would like to acknowledge the support of the National Natural Science Foundation of China(41974127,42174147).References。
文摘Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.
文摘Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.
文摘The magnetoresistance effect of a p-n junction under an electric field which is introduced by the gate voltage at room temperature is investigated by simulation. As auxiliary models, the Lombardi CVT model and carrier generation- recombination model are introduced into a drift-diffusion transport model and carrier continuity equations. All the equa- tions are discretized by the finite-difference method and the box integration method and then solved by Newton iteration. Taking advantage of those models and methods, an abrupt junction with uniform doping is studied systematically, and the magnetoresistance as a function of doping concentration, SiO2 thickness and geometrical size is also investigated. The simulation results show that the magnetoresistance （MR） can be controlled substantially by the gate and is dependent on the polarity of the magnetic field.
文摘Independent component analysis （ICA） is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton＇s iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.
