Range Particle Algorithm Application in the Solving Inverse Problem of Line Source

2012 ◽  
Vol 532-533 ◽  
pp. 1492-1496
Author(s):  
Ke Guang Yu
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
High Precision ◽  
Line Source ◽  
Measured Data ◽  
Range Searching ◽  
Computational Stability ◽  
Mathematical Solution ◽  
Source Particle ◽  
Implementation Steps

Now mature and effective algorithms for the numerical solution of inverse problem of line source are few, so the researching of algorithms for the problem is urgent and necessary. Firstly, a brief introduction to the characteristics of solving the inverse problem of the line source is given, and the mathematical solution model of inverse problem is established based on the Line source equation, Secondly a new algorithm (Range Particle algorithm) based on range searching algorithm is proposed for the numerical solving the inverse problem of the line source particle and the basic implementation steps and parameter adjustment of the algorithm also be discussed. Finally, simulated and measured data were used to test the effect of the algorithm. The results show that the range particle algorithm is an algorithm of high precision, fast convergence and computational stability for the solving the inverse problem of the line source and it do can be applied in Engineering.

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

scholarly journals Numerical Solution of the Spinor-Spinor Bethe-Salpeter Equation in Functional Nonlinear Spinor Theory

1975 ◽  
Vol 30 (5) ◽  
pp. 656-671
Author(s):  
W. Bauhoff
Keyword(s):  
Angular Momentum ◽  
Excited State ◽  
Variational Method ◽  
Numerical Solution ◽  
High Precision ◽  
Nonlinear Spinor ◽  
Spinor Theory ◽  
First Order ◽  
Scalar Mesons ◽  
Functional Methods

AbstractThe mass eigenvalue equation for mesons in nonlinear spinor theory is derived by functional methods. In second order it leads to a spinorial Bethe-Salpeter equation. This is solved by a variational method with high precision for arbitrary angular momentum. The results for scalar mesons show a shift of the first order results, obtained earlier. The agreement with experiment is improved thereby. An excited state corresponding to the η' is found. A calculation of a Regge trajectory is included,too.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

Settlement Prediction of Roadbed Based on Mixture Model with Exponential Curve and ANN

2013 ◽  
Vol 663 ◽  
pp. 76-79 ◽  
Author(s):  
Guo Heng Li ◽  
Han Bing Liu ◽  
Xu Xi Qin
Keyword(s):  
Mixture Model ◽  
High Precision ◽  
Measured Data ◽  
New Method ◽  
Settlement Prediction ◽  
Exponential Curve ◽  
Network Scale

A mixture method based on exponential curve and ANN is presented according to settlement prediction of roadbed with measured data. Based on this method, the rule of roadbed settlement is classified into sure part and uncertain part. Exponential curve is used to model the sure part, and ANN to model the uncertain part, thus the mixture settlement model can be obtained. Prediction results show that the mixture model has advantages of high precision and small network scale; it provides a new method for settlement prediction of roadbed.

Numerical Solution of the Inverse Problem of Self-Diffusion

2003 ◽  
Vol 30 (5) ◽  
pp. 53-54
Author(s):  
S. M. Usmanov ◽  
E. D. Shakir'yanov ◽  
G. E. Zaikov
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Self Diffusion
Sign in / Sign up

Export Citation Format

Share Document