scholarly journals Exponentially fitted multisymplectic scheme for conservative Maxwell equations with oscillary solutions

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0256108
Author(s):  
Xiuling Yin ◽  
Yanqin Liu ◽  
Jingjing Zhang ◽  
Yanfeng Shen ◽  
Limei Yan
Keyword(s):  
Maxwell Equations ◽  
Least Square Method ◽  
Measured Data ◽  
Numerical Results ◽  
Least Square ◽  
Stability And Convergence ◽  
One Dimension ◽  
Random Disturbance ◽  
Oscillatory Solutions ◽  
Exponentially Fitted

Aiming at conservative Maxwell equations with periodic oscillatory solutions, we adopt exponentially fitted trapezoidal scheme to approximate the temporal and spatial derivatives. The scheme is a multisymplectic scheme. Under periodic boundary condition, the scheme satisfies two discrete energy conservation laws. The scheme also preserves two discrete divergences. To reduce computation cost, we split the original Maxwell equations into three local one-dimension (LOD) Maxwell equations. Then exponentially fitted trapezoidal scheme, applied to the resulted LOD equations, generates LOD multisymplectic scheme. We prove the unconditional stability and convergence of the LOD multisymplectic scheme. Convergence of numerical dispersion relation is also analyzed. At last, we present two numerical examples with periodic oscillatory solutions to confirm the theoretical analysis. Numerical results indicate that the LOD multisymplectic scheme is efficient, stable and conservative in solving conservative Maxwell equations with oscillatory solutions. In addition, to one-dimension Maxwell equations, we apply least square method and LOD multisymplectic scheme to fit the electric permittivity by using exact solution disturbed with small random errors as measured data. Numerical results of parameter inversion fit well with measured data, which shows that least square method combined with LOD multisymplectic scheme is efficient to estimate the model parameter under small random disturbance.

scholarly journals Solution of inverse heat conduction equation with the use of Chebyshev polynomials

2016 ◽  
Vol 37 (4) ◽  
pp. 73-88 ◽  
Author(s):  
Magda Joachimiak ◽  
Andrzej Frąckowiak ◽  
Michał Ciałkowski
Keyword(s):  
Inverse Problem ◽  
Chebyshev Polynomials ◽  
Direct Problem ◽  
Least Square Method ◽  
Least Square ◽  
Random Disturbance ◽  
Inverse Heat Conduction ◽  
Chebyshev Nodes ◽  
The Difference ◽  
The Stability

AbstractA direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials. Calculations were made for a grid consisting of Chebyshev nodes, what allows us to use orthogonal properties of Chebyshev polynomials. Temperature distributions on the boundary for the inverse problem were determined using minimization of the functional being the measure of the difference between the measured and calculated values of temperature (boundary inverse problem). For the quasi-Cauchy problem, the distance between set values of temperature and heat flux on the boundary was minimized using the least square method. Influence of the value of random disturbance to the temperature measurement, of measurement points (distance from the boundary, where the temperature is not known) arrangement as well as of the thermocouple installation error on the stability of the inverse problem was analyzed.

Ultrasonic Detection Algorithm Research on the Damage Depth of Concrete after Fire

2011 ◽  
Vol 368-373 ◽  
pp. 2229-2234
Author(s):  
Jiang Tao Yu ◽  
Yuan Liu ◽  
Zhou Dao Lu ◽  
Peng Zhao
Keyword(s):  
Ultrasonic Method ◽  
Least Square Method ◽  
Detection Algorithm ◽  
Measured Data ◽  
Structural Member ◽  
Least Square ◽  
Propagation Time ◽  
Practical Application ◽  
Ultrasonic Detection ◽  
Damage Depth

To measure the depth of fire-damaged concrete by ultrasonic method, it was traditionally assumed that the concrete of the fire-damaged structural member could be simply classified into damaged layer and undamaged layer. Based on it, the damage depth can be calculated with a series of single-sided ultrasonic measured data. This method is simple and convenient but less accurate in the practical application. To improve the algorithm, hyperbola curves are adopted to simulate the varying of damage with depth in this paper. And parabolic curves are adopted to simulate the traces of ultrasonic wave in different measured distances. Therefore, the minimum propagation time can be obtained under different damage conditions. Through comparing the calculating results and measured data in different measured distances, the most likely damaged trend can be determined with least square method. At the end of this paper, examples are demonstrated to prove this algorithm feasible and more accurate than the traditional one.

scholarly journals An Improved Sequential Initiation Method for Multitarget Track in Clutter with Large Noise Measurement

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Daxiong Ji ◽  
Dongdong Li
Keyword(s):  
Least Square Method ◽  
Initial Position ◽  
Measured Data ◽  
Least Square ◽  
Multiple Objects ◽  
Detection Distance ◽  
Sequential Method ◽  
Sonar Sensors ◽  
Underwater Environment ◽  
Linear Least Square

This paper proposes an improved sequential method for underwater multiple objects tracks initiation in clutter, estimating the initial position for the trajectory. The underwater environment is complex and changeable, and the sonar data are not very ideal. When the detection distance is far, the error of measured data is also great. Besides that, the clutter has a grave effect on the tracks initiation. So it is hard to initialize a track and estimate the initial position. The new tracks initiation is that when at least six of ten points meet the requirements, then we determine that there is a new track and the initial states of the parameters are estimated by the linear least square method. Compared to the conventional tracks initiation methods, our method not only considers the kinematics information of targets, but also regards the error of the sonar sensors as an important element. Computer simulations confirm that the performance of our method is very nice.

The Novel Calibration Method for 3-DOF Measurement System

2011 ◽  
Vol 120 ◽  
pp. 440-443
Author(s):  
Kwang Il Lee ◽  
Jin Seok Jang ◽  
Hyun Woo Lee ◽  
Suk Jin Kim ◽  
Sang Ryong Lee ◽  
...  
Keyword(s):  
Measurement System ◽  
Measurement Accuracy ◽  
Least Square Method ◽  
Calibration Method ◽  
Measured Data ◽  
Least Square ◽  
The Novel ◽  
Squareness Error ◽  
Misalignment Error ◽  
Calibration Parameters

In this paper, a novel calibration method is developed to improve the measurement accuracy of 3-DOF measurement system. The squareness error between three sensors and misalignment error with respect to reference coordinate of machine tool are calibration parameters. To estimate these parameters, reference ball is used and moved in the measuring ranges of 3-DOF measurement system. The relation between calibration parameters, position of reference ball, measured data of sensors are defined using geometric constraint and estimated using least square method. Finally, simulation is done to check the feasibility of developed calibration method. The result of simulation revealed the validation of developed method.

Thermal Error Compensation and Modeling for CNC Boring and Milling Center

2014 ◽  
Vol 945-949 ◽  
pp. 1665-1668
Author(s):  
Jun Sun ◽  
Yan Ping Xu ◽  
Xing Liu
Keyword(s):  
Error Compensation ◽  
Structural Characteristics ◽  
Thermal Error ◽  
Least Square Method ◽  
Measured Data ◽  
Least Square ◽  
Model Parameters ◽  
Heat Sources ◽  
Thermal Error Model ◽  
Thermal Error Compensation

The thermal error compensation and modeling is an effective way to improve the machining tool precision. This article took the CNC boring and milling center for example. Firstly, this article made analysis and research on the heat sources by analyzing the structural characteristics of CNC boring and milling center, and then on the basis of the previously measured data of selected critical temperature points, established the thermal error model using a method of multiple linear regression based on least square method. The model parameters were solved by MATLAB software. Finally, thermal error compensation model was tested.

Research on Course Radius Measurement for Vertical Petroleum Tank Volume Metrology Based on 3D Laser Scan Principle

2010 ◽  
Vol 439-440 ◽  
pp. 983-988
Author(s):  
Jin Tao Wang ◽  
Zi Yong Liu ◽  
Long Zhang ◽  
Li Gong Guo ◽  
Xue Song Bao ◽  
...  
Keyword(s):  
Phase Shift ◽  
Measurement Method ◽  
Least Square Method ◽  
Measured Data ◽  
Least Square ◽  
Point Location ◽  
Equivalent Radius ◽  
Optical Grating ◽  
Maximal Deviation ◽  
Mandatory Standard

One course radius measurement method for vertical petroleum tank volume metrology based on 3D laser scan principle was researched. Method of distance measurement by laser phase-shift technology and angular measurement by optical grating was applied to acquire coordinates of points in each course under the control of servo system. The permitted error of measured point location is 2mm. Fitting algorithms base on direct iterative method (DIM) and least square method (LSM) were used to process measured data and deduce equivalent radius of each course. In comparison experiment, one 1000m3 vertical tank was used as test object. Compared to strapping method (international mandatory standard), the maximal deviation radius value of method discussed is 2.8mm. The maximal difference of radius value calculated by DIM and LSM is 0.1mm. The experimental results verified the method discussed in this paper.

Research on Characteristics of Horizontal Atmospheric Diffusion Coefficient Based on BP Neural Network

2013 ◽  
Vol 791-793 ◽  
pp. 1605-1608 ◽  
Author(s):  
Pin Shang ◽  
Cheng Dong Wu ◽  
Ren Ke Han ◽  
Wen Jia Ma
Keyword(s):  
Neural Network ◽  
Diffusion Coefficient ◽  
Bp Neural Network ◽  
Characteristic Curve ◽  
Least Square Method ◽  
Measured Data ◽  
Least Square ◽  
Atmospheric Diffusion ◽  
Actual Application ◽  
Trained Neural Network

In order to obtain the actual characteristics of horizontal atmospheric diffusion direction, based on Gauss plume model and the measured data, we use BP neural network to fit the characteristic curve of the diffusion coefficient. We establish a BP neural network, and then we train the network and simulate the diffusion coefficient. According to the simulation results, we compare the characteristic curve with the curve based on the least square method. And the results show that the characteristic curve based on BP neural network has better fitting accuracy. Hence, using the trained neural network to predict the diffusion coefficient has certain theory meaning and actual application value.

Research on Course Radius Measurement for Vertical Petroleum Tank Volume Metrology Based on 3D Laser Scan Principle

2010 ◽  
Vol 439-440 ◽  
pp. 1105-1110
Author(s):  
Jin Tao Wang ◽  
Zi Yong Liu ◽  
Long Zhang ◽  
Li Gong Guo ◽  
Xue Song Bao ◽  
...  
Keyword(s):  
Phase Shift ◽  
Measurement Method ◽  
Least Square Method ◽  
Measured Data ◽  
Least Square ◽  
Point Location ◽  
Equivalent Radius ◽  
Optical Grating ◽  
Maximal Deviation ◽  
Mandatory Standard

One course radius measurement method for vertical petroleum tank volume metrology based on 3D laser scan principle was researched. Method of distance measurement by laser phase-shift technology and angular measurement by optical grating was applied to acquire coordinates of points in each course under the control of servo system. The permitted error of measured point location is 2mm. Fitting algorithms base on direct iterative method (DIM) and least square method (LSM) were used to process measured data and deduce equivalent radius of each course. In comparison experiment, one 1000m3 vertical tank was used as test object. Compared to strapping method (international mandatory standard), the maximal deviation radius value of method discussed is 2.8mm. The maximal difference of radius value calculated by DIM and LSM is 0.1mm. The experimental results verified the method discussed in this paper.

Development of Non-Contact Online Measuring System for Middle-Convex and Varying Ellipse Piston

2013 ◽  
Vol 753-755 ◽  
pp. 2282-2285
Author(s):  
Dong Zheng ◽  
Hui Xing Zhou ◽  
Han Wu ◽  
Chao Yang Zhang
Keyword(s):  
Digital Signal Processor ◽  
Digital Signal ◽  
Least Square Method ◽  
High Accuracy ◽  
Measured Data ◽  
Least Square ◽  
Measuring System ◽  
Displacement Sensor ◽  
Contour Error ◽  
Laser Displacement Sensor

A non-contact online measuring system is developed to measure the contour error of the middle-convex and varying ellipse piston. A high accuracy laser displacement sensor is used to measure the elliptical profiles of the piston, and a measuring collector is designed based on digital signal processor (DSP) TMS320F28335 to ensure strict correspondence between the angles and the radii data of the sampling points. The measured data is analyzed with least square method to calculate the contour error of the pistons cross section. The reliability of the measuring system is proved by experiment.

Direct Assessment of Effective Renal Plasma Flow from Renoscintigraphy with a Gamma Camera and an On-Line Computer

1981 ◽  
Vol 20 (06) ◽  
pp. 274-278
Author(s):  
J. Liniecki ◽  
J. Bialobrzeski ◽  
Ewa Mlodkowska ◽  
M. J. Surma
Keyword(s):  
Count Rate ◽  
Renal Plasma Flow ◽  
Early Period ◽  
Least Square Method ◽  
Least Square ◽  
Uptake Coefficient ◽  
Positive Linear Correlation ◽  
On Line ◽  
Best Fit ◽  
Plasma Activity

A concept of a kidney uptake coefficient (UC) of 131I-o-hippurate was developed by analogy from the corresponding kidney clearance of blood plasma in the early period after injection of the hippurate. The UC for each kidney was defined as the count-rate over its ROI at a time shorter than the peak in the renoscintigraphic curve divided by the integral of the count-rate curve over the "blood"-ROI. A procedure for normalization of both curves against each other was also developed. The total kidney clearance of the hippurate was determined from the function of plasma activity concentration vs. time after a single injection; the determinations were made at 5, 10, 15, 20, 30, 45, 60, 75 and 90 min after intravenous administration of 131I-o-hippurate and the best-fit curve was obtained by means of the least-square method. When the UC was related to the absolute value of the clearance a positive linear correlation was found (r = 0.922, ρ > 0.99). Using this regression equation the clearance could be estimated in reverse from the uptake coefficient calculated solely on the basis of the renoscintigraphic curves without blood sampling. The errors of the estimate are compatible with the requirement of a fast appraisal of renal function for purposes of clinical diagknosis.

Sign in / Sign up

Export Citation Format

Share Document