Proper Generalized Decomposition Method for Solving Fisher-Type Equation and Heat Equation

Isaac, Chukwuemeke William

doi:10.1134/s2070048218010039

Cited by 2 publications

(1 citation statement)

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“…The IHCP (Hadamard and Morse, 1953;Beck and Woodbury, 2016;Lin and Yang, 2007) is a heat transfer problem whose outcomes are difficult to measure. Since Stolz (Stolz, 1960) published the first paper on the IHCP in 1960, many scientists have explored numerical solutions to the IHCP, such as Tikhonov's regularization method (Qiao et al, 2017), Beck's serialization method, Blackwell's time-marching algorithm method, Weber's space propulsion algorithm method (Blackwell, 1981), Elden's Fourier regularization method (Weber, 1981), and the conjugate gradient method (Isaac, 2018;Amini et al, 2018;Dehghani and Mahdavi-Amiri, 2018). Through these methods, the IHCP has undergone significant advancement in practical engineering and scientific experiment and measurement.…”

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confidence: 99%

Numerical Simulation for Inverse Heat Conduction Problem of Single-Layer Lining Erosion of Blast Furnace

Su¹,

Song²,

Ni³

et al. 2019

Frontiers in Heat and Mass Transfer

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A mathematical model of the inverse heat transfer problem of blast furnace lining is established in this study. Following the identification of the boundary conditions of the model, the inverse problem via the conjugate gradient method was decomposed into three issues: the direct problem, the sensitivity problem, and the adjoint problem. The feasibility of the model was verified through two types of real inner wall boundary shape functions. The effects of the initial inner wall boundary shape function and the number of measuring points are also investigated. Results showed that the accuracy of the inverse solution is independent of the initial inner wall boundary shape function. The number of measuring points exerts some influence on the inversion results. That is, a large number of measuring points equates to a good capture of curves, but an accurate inverse solution also can be obtained with few measuring points, although arranging a large number of points can achieve a slightly better solution. The average relative error of this solution is approximately 3%.

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