TY - JOUR

T1 - Meshless local petrov-galerkin mixed collocation method for solving cauchy inverse problems of steady-state heat transfer

AU - Zhang, Tao

AU - He, Yiqian

AU - Dong, Leiting

AU - Li, Shu

AU - Alotaibi, Abdullah

AU - Atluri, Satya N.

PY - 2014

Y1 - 2014

N2 - In this article, the Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed to solve the Cauchy inverse problems of Steady- State Heat Transfer In the MLPG mixed collocation method, the mixed scheme is applied to independently interpolate temperature as well as heat flux using the same meshless basis functions The balance and compatibility equations are satisfied at each node in a strong sense using the collocation method. The boundary conditions are also enforced using the collocation method, allowing temperature and heat flux to be over-specified at the same portion of the boundary. For the inverse problems where noise is present in the measurement, Tikhonov regularization method is used, to mitigate the inherent ill-posed nature of inverse problem, with its regularization parameter determined by the L-Curve method. Several numerical examples are given, wherein both temperature as well as heat flux are prescribed at part of the boundary, and the data at the other part of the boundary and in the domain have to be solved for. Through these numerical examples, we investigate the accuracy, convergence, and stability of the proposed MLPG mixed collocation method for solving inverse problems of Heat Transfer.

AB - In this article, the Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed to solve the Cauchy inverse problems of Steady- State Heat Transfer In the MLPG mixed collocation method, the mixed scheme is applied to independently interpolate temperature as well as heat flux using the same meshless basis functions The balance and compatibility equations are satisfied at each node in a strong sense using the collocation method. The boundary conditions are also enforced using the collocation method, allowing temperature and heat flux to be over-specified at the same portion of the boundary. For the inverse problems where noise is present in the measurement, Tikhonov regularization method is used, to mitigate the inherent ill-posed nature of inverse problem, with its regularization parameter determined by the L-Curve method. Several numerical examples are given, wherein both temperature as well as heat flux are prescribed at part of the boundary, and the data at the other part of the boundary and in the domain have to be solved for. Through these numerical examples, we investigate the accuracy, convergence, and stability of the proposed MLPG mixed collocation method for solving inverse problems of Heat Transfer.

KW - Collocation

KW - Heat transfer

KW - Inverse problem

KW - MLPG

UR - http://www.scopus.com/inward/record.url?scp=84900393953&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84900393953

VL - 97

SP - 509

EP - 533

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 6

ER -