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• W2077725801 abstract "In this paper the iterative algorithm proposed by Kozlov et al. for the Cauchy problem for the Laplace equation is extended in order to solve the Cauchy steady-state heat conduction problem in an anisotropic medium. The iterative algorithm is numerically implemented using the boundary element method (BEM). The convergence and the stability of the numerical method, as well as various types of accuracy, convergence and stopping criteria, are investigated. The numerical results obtained confirm that provided an appropriate stopping regularization criterion is imposed, then the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularization criterion to cease the iterative process is proposed and the rate of convergence of the algorithm is improved by using various relaxation procedures between iterations. A new concept of a variable relaxation factor is proposed. Analytical formulae for the coefficients of the matrices resulting from the direct application of the BEM in an anisotropic medium are also presented. Copyright © 2000 John Wiley & Sons, Ltd." @default.
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• W2077725801 date "2000-01-01" @default.
• W2077725801 modified "2023-10-14" @default.
• W2077725801 title "The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium" @default.
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• W2077725801 doi "https://doi.org/10.1002/1097-0207(20001010)49:4<481::aid-nme970>3.0.co;2-5" @default.
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