INVERSION OF THE INNER WALL TEMPERATURE OF THE TWO-DIMENSIONAL PIPE BASED ON CONJUGATE GRADIENT METHOD

2018 ◽  
Author(s):  
Ping Xiong ◽  
Tao Lu ◽  
Bo Liu
Keyword(s):  
Conjugate Gradient Method ◽  
Wall Temperature ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Two Dimensional

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.

Construction of a Preconditioner for General Elliptic Problems Using Riesz Map

2020 ◽  
Vol 18 (01) ◽  
pp. 2050031
Author(s):  
Raghia El Hanine ◽  
Said Raghay ◽  
Hassane Sadok
Keyword(s):  
Hilbert Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Two Dimensional ◽  
General Elliptic ◽  
Symmetric Systems

The current work aspires to design and study the construction of an efficient preconditioner for linear symmetric systems in a Hilbert space setting. Compliantly to Josef Málek and Zdeněk Strakoš’s work [Preconditioning and the Conjugate Gradient Method in the Context of Solving[Formula: see text] PDEs, Vol. 1 (SIAM, USA).], we shed new light on the dependence of algebraic preconditioners with the resolution steps of partial differential equations (PDEs) and describe their impact on the final numerical solution. The numerical strength and efficiency of the proposed approach is demonstrated on a two-dimensional examples.

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