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Article Citation - Scopus: 2A New Formulation for the Boundary Element Analysis of Heat Conduction Problems With Nonlinear Boundary Conditions;(Turk Isı Bilimi ve Teknigi Dernegi, 2019) Baranoğlu,B.An effective numerical method based on the boundary element formulation is presented to solve heat conduction equations which are governed by the Fourier equation, with nonlinear boundary conditions on one or more sections of the prescribed boundary. The solution involves the manipulation of the system matrices of the boundary element method and obtaining a smaller ranked matrix equation in which the unknown is only the temperature difference over the nonlinear boundary condition region. This way, the iterations to deal with the nonlinear conditions are performed faster. After finding the solution over the nonlinear boundary condition region, the solution over the entire boundary is obtained as a post-process through a prescribed relation. An example with a proven exact solution is employed to assess the results. © 2019 TIBTD Printed in TurkeyArticle An Adaptive Element Division Algorithm for Accurate Evaluation of Singular and Near Singular Integrals in 3d(Turkiye Klinikleri, 2021) Bayindir,H.; Baranoğlu,B.; Yazici,A.An adaptive algorithm for evaluation of singular and near singular integrals in 3D is presented. The algorithm is based on successive adaptive/selective subdivisions of the element until a prescribed error criteria is met. For evaluating the integrals in each subdivision, Gauss quadrature is applied. The method is computationally simple, memory efficient and can be applied for both triangular and quadrilateral elements, including the elements with nonplanar and/or curved surfaces. To assess the method, several examples are discussed. It has shown that the algorithm performs well for singular and near-singular integral examples presented in the paper and evaluates the integrals with very high accuracy. © TÜBİTAK
