Numerical solution of the Cauchy problem for steady-state heat transfer in two-dimensional functionally graded materials |
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| Affiliation: | 1. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus;2. Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK;3. Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei, 010014 Bucharest, Romania;4. Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, 010141 Bucharest, Romania;1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;2. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China |
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| Abstract: | The application of the method of fundamental solutions to the Cauchy problem for steady-state heat conduction in two-dimensional functionally graded materials (FGMs) is investigated. The resulting system of linear algebraic equations is ill-conditioned and, therefore, regularization is required in order to solve this system of equations in a stable manner. This is achieved by employing the zeroth-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for both smooth and piecewise smooth geometries. The convergence and the stability of the method with respect to increasing the number of source points and the distance between the source points and the boundary of the solution domain, and decreasing the amount of noise added into the input data, respectively, are analysed. |
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