scholarly journals Error Estimate and Adaptive Refinement in Mixed Discrete Least Squares Meshless Method

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
J. Amani ◽  
A. Saboor Bagherzadeh ◽  
T. Rabczuk
Keyword(s):  
Convergence Rate ◽  
Error Estimate ◽  
Least Squares ◽  
Meshless Method ◽  
Least Square ◽  
Adaptive Refinement ◽  
Error Estimator ◽  
Shape Functions ◽  
Numerical Errors ◽  
Elasticity Problems

The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.

scholarly journals A new meshless method using Taylor series to solve elasticity problems

2012 ◽  
Author(s):  
Yendoubouam Tampango ◽  
Michel Potier-Ferry ◽  
Yao Koutsawa ◽  
Salim Belouettar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Taylor Series ◽  
Meshless Method ◽  
Classical Method ◽  
Taylor Series Expansion ◽  
Least Square Method ◽  
Least Square ◽  
Radius Of Convergence ◽  
Elasticity Problems

A meshless method is presented and analysed. In this approach, one discretises only the boundary, the partial differential equation being solved in the domain by using Taylor series expansion. A least square method is used to apply boundary conditions. In this paper, the method is applied to Navier equations for linear elasticity. Various tests are presented to discuss the efficiency and robustness of the method. The convergence is exponential with respect to the degree but it depends on the radius of convergence of the series. That is why an algorithm has been associated with the Domb–Sykes plot that is a classical method to detect singularities and evaluate the radius of convergence.

scholarly journals AN ELASTO-PLASTIC ANALYSIS OF SOLIDS BY THE LOCAL MESHLESS METHOD BASED ON MLS

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5780-5786 ◽  
Author(s):  
Y.T. GU
Keyword(s):  
Meshless Method ◽  
Deformation Theory ◽  
Weak Form ◽  
Least Square ◽  
Shape Functions ◽  
Total Deformation ◽  
Moving Least Square ◽  
Numerical Studies ◽  
Plastic Analysis ◽  
Local Weak Form

A pseudo-elastic local meshless formulation is developed in this paper for elasto-plastic analysis of solids. The moving least square (MLS) is used to construct the meshless shape functions, and the weighted local weak-form is employed to derive the system of equations. Hencky's total deformation theory is applied to define the effective Young's modulus and Poisson's ratio in the nonlinear analysis, which are obtained in an iterative manner using the strain controlled projection method. Numerical studies are presented for the elasto-plastic analysis of solids by the newly developed meshless formulation. It has demonstrated that the present pseudo-elastic local meshless approach is very effective for the elasto-plastic analysis of solids.

Improving Space-Time-Frequency MIMO-OFDM with ICI Self-Cancellation Scheme using Least Square Error Estimator

2015 ◽  
Vol 12 (1) ◽  
pp. 25
Author(s):  
Nur Farahiah Ibrahim ◽  
Zahari Abu Bakar ◽  
Azlina Idris
Keyword(s):  
Channel Estimation ◽  
Orthogonal Frequency Division Multiplexing ◽  
Symbol Error Rate ◽  
Space Time ◽  
Least Square ◽  
Error Estimator ◽  
Frequency Diversity ◽  
Time Frequency ◽  
Mimo Ofdm ◽  
Subcarrier Mapping

Channel estimation techniques for Multiple-input Multiple-output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) based on comb type pilot arrangement with least-square error (LSE) estimator was investigated with space-time-frequency (STF) diversity implementation. The frequency offset in OFDM effected its performance. This was mitigated with the implementation of the presented inter-carrier interference self-cancellation (ICI-SC) techniques and different space-time subcarrier mapping. STF block coding in the system exploits the spatial, temporal and frequency diversity to improve performance. Estimated channel was fed into a decoder which combined the STF decoding together with the estimated channel coefficients using LSE estimator for equalization. The performance of the system was compared by measuring the symbol error rate with a PSK-16 and PSK-32. The results show that subcarrier mapping together with ICI-SC were able to increase the system performance. Introduction of channel estimation was also able to estimate the channel coefficient at only 5dB difference with a perfectly known channel.

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

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