Trefftz method for a polynomial-based boundary identification in two-dimensional Laplacian problems
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Kielce University of Technology, Faculty of Management and Computer Modelling, Kielce
Publication date: 2016-07-17
Journal of Theoretical and Applied Mechanics 2016;54(3):935–944
The paper addresses a two-dimensional boundary identification (reconstruction) problem in steady-state heat conduction. Having found the solution to the Laplace equation by superpositioning T-complete functions, the unknown boundary of a plane region is approximated by polynomials of an increasing degree. The provided examples indicate that sufficient accuracy can be obtained with a use of polynomials of a relatively low degree, which allows avoidance of large systems of nonlinear equations. Numerical simulations for assessing the performance of the proposed algorithm show better than 1% accuracy after a few iterations and very low sensitivity to small data errors.