scholarly journals MFS fading regularization method for the identification of boundary conditions from partial elastic displacement field data

2018 ◽  
Author(s):  
L. Caillé ◽  
J L. Hanus ◽  
F. Delvare ◽  
N. Michaux-Leblonda
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Regularization Method ◽  
Synthetic Data ◽  
Fundamental Solutions ◽  
Image Correlation ◽  
Method Of Fundamental Solutions ◽  
Elastic Displacement ◽  
Isotropic Elasticity

A method is proposed to solve an inverse problem in twodimensional linear isotropic elasticity. The inverse problem consists of the determination of both the entire displacement field and the boundary conditions inaccessible to the measurement from the partial knowledge of the displacement field. The algorithm is based on a fading regularization method (FRM) and is numerically implemented using the method of fundamental solutions (MFS). The inverse technique is first validated with synthetic data and is then applied to the interpretation of experimental measurements obtained by digital image correlation (DIC).

A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

2013 ◽  
Vol 5 (06) ◽  
pp. 825-845 ◽  
Author(s):  
B. Tomas Johansson ◽  
Daniel Lesnic ◽  
Thomas Reeve
Keyword(s):  
Stefan Problem ◽  
Regularization Method ◽  
Input Data ◽  
Stable Solution ◽  
Higher Dimensions ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Two Dimensional ◽  
Two Phase ◽  
Ill Posed

AbstractIn this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.

Solution of direct and inverse conduction heat transfer problems using the method of fundamental solutions and differential evolution

2020 ◽  
Vol 37 (9) ◽  
pp. 3293-3319
Author(s):  
Adam Basílio ◽  
Fran Sérgio Lobato ◽  
Fábio de Oliveira Arouca
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Evolution ◽  
Computational Cost ◽  
Differential Evolution Algorithm ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Content Type ◽  
Evolution Algorithm

Purpose The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented by partial differential equations associated with initial and boundary conditions. In general, the resolution of these problems requires using numerical techniques through discretization of boundary and internal points of the domain considered, implying a high computational cost. As an alternative to reducing computational costs, various approaches based on meshless (or meshfree) methods have been evaluated in the literature. In this contribution, the purpose of this paper is to formulate and solve direct and inverse problems applied to Laplace’s equation (steady state and bi-dimensional) considering different geometries and regularization techniques. For this purpose, the method of fundamental solutions is associated to Tikhonov regularization or the singular value decomposition method for solving the direct problem and the differential Evolution algorithm is considered as an optimization tool for solving the inverse problem. From the obtained results, it was observed that using a regularization technique is very important for obtaining a reliable solution. Concerning the inverse problem, it was concluded that the results obtained by the proposed methodology were considered satisfactory, as even with different levels of noise, good estimates for design variables in proposed inverse problems were obtained. Design/methodology/approach In this contribution, the method of fundamental solution is used to solve inverse problems considering the Laplace equation. Findings In general, the proposed methodology was able to solve inverse problems considering different geometries. Originality/value The association between the differential evolution algorithm and the method of fundamental solutions is the major contribution.

scholarly journals Numerical Stability Investigations of the Method of Fundamental Solutions Applied to Wave-Current Interactions Using Generating-Absorbing Boundary Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1153
Author(s):  
Mohammed Loukili ◽  
Denys Dutykh ◽  
Kamila Kotrasova ◽  
Dezhi Ning
Keyword(s):  
Boundary Conditions ◽  
Fundamental Solutions ◽  
Absorbing Boundary Conditions ◽  
Method Of Fundamental Solutions ◽  
Use Case ◽  
Numerical Wave Tank ◽  
Absorbing Boundary ◽  
Numerical Wave ◽  
The Stability ◽  
Water Depths

In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to the wave-current interactions is investigated using the Method of Fundamental Solutions (MFS), in a Numerical Wave Tank (NWT) within the potential theory where the main regular manifestations are the periodicity, and symmetry of traveling waves. Besides, the investigations cover different aspects of currents (coplanar current, without current, and opposing current), and also different water depths. Furthermore, the accuracy and stability of the numerical method (MFS) used in this work is evaluated for different locations and numbers of source points.

An Inverse Problem in Elasticity With Partially Overprescribed Boundary Conditions, Part I: Theoretical Approach

1993 ◽  
Vol 60 (3) ◽  
pp. 595-600 ◽  
Author(s):  
Weichung Yeih ◽  
Tatsuhito Koya ◽  
Toshio Mura
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Cauchy Problem ◽  
Boundary Conditions ◽  
Linear Elasticity ◽  
Fredholm Integral Equation ◽  
Theoretical Approach ◽  
Regularization Method ◽  
Numerical Examples

A Cauchy problem in linear elasticity is considered. This problem is governed by a Fredholm integral equation of the first kind and cannot be solved directly. The regularization method, which has been originally employed by Gao and Mura (1989), is formulated from a different perspective in order to address some of the difficulties experienced in their formulation. The theoretical details are discussed in this paper. Numerical examples are treated to Part II.

Sign in / Sign up

Export Citation Format

Share Document