Non-Linear Localization Algorithm Based on Newton Iterations

In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of time difference of arrival,the location estimation is expressed as an optimal problem of a non-linear programming.Then,an initial point is obtained using the semi-definite programming.And finally,the location is extracted from the local optimal solution acquired by Newton iterations.Simulation results show that when the number of anchor nodes is large,the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

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.

Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations

This paper presents mechanical quadrature methods (MQMs) for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O(h 3 ) and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h 3 -Richardson extrapolation algorithms (EAs), the accuracy to the order of O(h 5 ) is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.

Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm

In this paper,we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves.The algorithm relies on the Frechet differentiability analysis of the locally rough surface scattering problem,which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data.With a slight modification,the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface.Finally,numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.

A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

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.

On Direct and Semi-Direct Inverse of Stokes,Helmholtz and Laplacian Operators in View of Time-Stepper-Based Newton and Arnoldi Solvers in Incompressible CFD

Factorization of the incompressible Stokes operator linking pressure and velocity is revisited.The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability.It is shown that the Stokes operator can be inversed within an acceptable computational effort.This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix.It is shown,additionally,that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers,as well as for other problems where convergence of iterative methods slows down.Implementation of the Stokes operator inverse to time-steppingbased formulation of the Newton and Arnoldi iterations is discussed.

A Generalized Numerical Approach for Modeling Multiphase Flow and Transport in Fractured Porous Media

A physically based numerical approach is presented for modeling multiphase flow and transport processes in fractured rock.In particular,a general framework model is discussed for dealing with fracture-matrix interactions,which is applicable to both continuum and discrete fracture conceptualization.The numerical modeling approach is based on a general multiple-continuum concept,suitable for modeling any types of fractured reservoirs,including double-,triple-,and other multiplecontinuum conceptual models.In addition,a new,physically correct numerical scheme is discussed to calculate multiphase flow between fractures and the matrix,using continuity of capillary pressure at the fracture-matrix interface.The proposed general modeling methodology is verified in special cases using analytical solutions and laboratory experimental data,and demonstrated for its application in modeling flow through fractured vuggy reservoirs.

An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids

A Newton/LU-SGS(lower-upper symmetric Gauss-Seidel)iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids.The Newton iteration was employed to solve the nonlinear system,while the linear system was solved with LU-SGS iteration.The effect of several parameters in the implicit scheme,such as the CFL number,the Newton sub-iteration steps,and the update frequency of Jacobian matrix,was investigated to evaluate the performance of convergence history.Several typical test cases were simulated,and compared with the traditional explicit Runge-Kutta(RK)scheme.Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes.Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also.Finally,the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity.The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently.Choosing proper parameters would improve the efficiency of the implicit scheme.Moreover,in the same framework,the DG/FV hybrid schemes are more efficient than the same order DG schemes.

Numerical Approximation of a Nonlinear 3D Heat Radiation Problem

In this paper,we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in IR^(3).We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem.Moreover,we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem.A numerical example is given to illustrate theoretical results.

New Algorithm for Fault Superimposed Quantities Based on Superimposed Network

A new algorithm for fault superimposed quantity(FSIQ)is presented and analyzed.The network equations are built up by combining fault superimposed networks(FSIN)with the boundary conditions of FSIQ at the fault point and are solved with the Newton iterative method.The algorithm has clear physical meaning and does not require an intermediate procedure to derive FSIQ.The algorithm is implemented by computer programming,and the results of calculations show that the algorithm is fast and accurate.The method can be used not only to calculate FSIQ in the complex power systems with simple or multiple faults,but also to analyze and evaluate the performance of the protective relays and automatic devices based on FSIQ.