Elastoplasticity 2D Problems: Numerical Applications of the Tikhonov Regularization Method

2015 ◽  
Vol 751 ◽  
pp. 109-117
Author(s):  
Thales Augusto Barbosa Pinto Silva ◽  
Hilbeth Parente Azikri de Deus ◽  
Claudio Roberto Ávila da Silva
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Numerical Approach ◽  
Theoretical Development ◽  
Tikhonov Regularization Method ◽  
Equilibrium Curve ◽  
Numerical Examples ◽  
Elastoplastic Materials ◽  
Ill Conditioning

The numerical simulation is widely used, in now days, to verify the viability and to optimize structural mechanic designs. The numerical approach of elastoplastic materials can found some problems related to ill-conditioning of matrices (from FEM systems), associated to the critical points from the snap through or snap back shape of the equilibrium curve. Aiming to overcome this misfortune it is proposed a strategy via Tikhonov regularization method in association with L-curve technique to determine the regularization parameter. This strategy can be used in many numerical applications for structural analysis. The theoretical development about these Some numerical examples are presented to attest the efficiency of this proposed approach.

scholarly journals EXTRAPOLATION OF TIKHONOV REGULARIZATION METHOD

2010 ◽  
Vol 15 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Uno Hämarik ◽  
Reimo Palm ◽  
Toomas Raus
Keyword(s):  
Approximate Solution ◽  
Tikhonov Regularization ◽  
Noise Level ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Noisy Data ◽  
Tikhonov Regularization Method ◽  
Guaranteed Accuracy ◽  
Numerical Examples ◽  
Ill Posed

We consider regularization of linear ill‐posed problem Au = f with noisy data fδ, ¦fδ - f¦≤ δ . The approximate solution is computed as the extrapolated Tikhonov approximation, which is a linear combination of n ≥ 2 Tikhonov approximations with different parameters. If the solution u* belongs to R((A*A) n ), then the maximal guaranteed accuracy of Tikhonov approximation is O(δ 2/3) versus accuracy O(δ 2n/(2n+1)) of corresponding extrapolated approximation. We propose several rules for choice of the regularization parameter, some of these are also good in case of moderate over‐ and underestimation of the noise level. Numerical examples are given.

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

The Regularization Method Based on Complex Collinearity Diagnostics and Metrics

2013 ◽  
Vol 416-417 ◽  
pp. 1393-1398
Author(s):  
Chao Zhong Ma ◽  
Yong Wei Gu ◽  
Ji Fu ◽  
Yuan Lu Du ◽  
Qing Ming Gui
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Measurement Data ◽  
Tikhonov Regularization Method ◽  
Parameter Determination ◽  
Selection Methods ◽  
Ill Posed ◽  
Collinearity Diagnostics ◽  
Regularization Matrix

In a large number of measurement data processing, the ill-posed problem is widespread. For such problems, this paper introduces the solution of ill-posed problem of the unity of expression and Tikhonov regularization method, and then to re-collinearity diagnostics and metrics based on proposed based on complex collinearity diagnostics and the metric regularization method is given regularization matrix selection methods and regularization parameter determination formulas. Finally, it uses a simulation example to verify the effectiveness of the method.

Comparison of Tikhonov Regularization and Adaptive Regularization for III-Posed Problems

2013 ◽  
Vol 380-384 ◽  
pp. 1193-1196
Author(s):  
Wen Dong ◽  
Tao Sun
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Information Science ◽  
Tikhonov Regularization Method ◽  
Adaptive Regularization ◽  
Numerical Examples ◽  
Close Relationship ◽  
Ill Posed ◽  
The Stability ◽  
Science Information

nverse problems are important interdisciplinary subject, which receive more and more attention in recent years in the areas of mathematics, computer science, information science and other applied natural sciences. There is close relationship between inverse problems and ill-posedness. Regularization is an important strategy when computing the ill-posed problems to maintain the stability of the computation.This paper compares a new regularization method,which is called Adaptive regularization, with the traditional Tikhonov regularization method. The conclusion that Adaptive regularization method is a stronger regularization method than the traditional Tikhonov regularization method can be made by computing some numerical examples.

A New Computational Inverse Method and Application to the Identification of Dynamic Loads

2013 ◽  
Vol 631-632 ◽  
pp. 1298-1302
Author(s):  
Lin Jun Wang ◽  
You Xiang Xie ◽  
Hai Hua Wu
Keyword(s):  
Tikhonov Regularization ◽  
Regularization Method ◽  
Present Method ◽  
Inverse Method ◽  
Regularization Parameter ◽  
A Priori ◽  
Identification Problem ◽  
Dynamic Loads ◽  
Tikhonov Regularization Method ◽  
Simply Supported

In this paper, we propose a new computational inverse method for solving the identification of multi-source dynamic loads acting on a simply supported plate. Using a priori choosing appropriate regularization parameter, the present method can obtain higher optimum asymptotic order of the regularized solution than ordinary Tikhonov regularization method. In the numerical simulations, the identification problem of multi-source dynamic loads on a surface of simply supported plate is successfully solved by the present method. Meanwhile, most of its performances are better than ordinary Tikhonov regularization method.

Sign in / Sign up

Export Citation Format

Share Document