Weichung Yeih1,2, I-Yao Chan1, Chia-Ming Fan1, Jiang-Jhy Chang1, Chein-Shan Liu3
CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.2, pp. 169-194, 2014, DOI:10.3970/cmes.2014.099.169
Abstract In this paper, the Cauchy inverse problem of the nonlinear steady-state heat equation is studied. The double iteration process is used to tackle this problem in which the outer loop is developed based on the residual norm based algorithm (RNBA) while the inner loop determines the evolution direction and the modified Tikhonov's regularization method (MTRM) developed by Liu (Liu, 2012) is adopted. For the conventional iteration processes, a fixed evolution direction such as F, B−1F, BTF or αF+(1-α)BTF is used where F is the residual vector, B is the Jacobian matrix, the superscript '-1' denotes the inverse, the superscript 'T'… More >
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