Identification of an unknown time-dependent heat source term from overspecified Dirichlet boundary data by conjugate gradient method

2013 ◽  
Vol 65 (1) ◽  
pp. 42-57 ◽  
Author(s):  
Alemdar Hasanov ◽  
Burhan Pektaş
Keyword(s):  
Heat Source ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Boundary Data ◽  
Source Term ◽  
Dirichlet Boundary ◽  
Time Dependent ◽  
Dirichlet Boundary Data

scholarly journals Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Shoubin Wang ◽  
Li Zhang ◽  
Xiaogang Sun ◽  
Huangchao Jia
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Measuring Error ◽  
Two Dimensional ◽  
Inverse Heat Transfer ◽  
Heat Transfer System ◽  
Transfer Problems

The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

scholarly journals Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids

2017 ◽  
Vol 17 (4) ◽  
pp. 739-767 ◽  
Author(s):  
Luan T. Hoang ◽  
Thinh T. Kieu
Keyword(s):  
Porous Media ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Time Derivative ◽  
Compressible Fluids ◽  
Time Dependent ◽  
Asymptotic Estimates ◽  
Slightly Compressible ◽  
Interior Estimates ◽  
Dirichlet Boundary Data

AbstractThe generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time, the interior {L^{\infty}}-estimates for the pressure, its gradient and time derivative, and the interior {L^{2}}-estimates for its Hessian. The De Giorgi and Ladyzhenskaya–Uraltseva iteration techniques are used taking into account the special structures of the equations for both pressure and its gradient. These are combined with the uniform Gronwall-type bounds in establishing the asymptotic estimates when time tends to infinity.

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