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https://hdl.handle.net/11147/6767
Title: | Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions | Authors: | Ivanyshyn Yaman, Olha Kress, Rainer |
Keywords: | Boundary integral equation Nonlinear equations Free boundary Laplace equation |
Publisher: | Elsevier Ltd. | Source: | Ivanyshyn Yaman, O., and Kress, R. (2017). Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions. Computers and Mathematics with Applications, 74(11), 2784-2791. doi:10.1016/j.camwa.2017.06.011 | Abstract: | In this paper we present a numerical solution method for the Bernoulli free boundary value problem for the Laplace equation in three dimensions. We extend a nonlinear integral equation approach for the free boundary reconstruction (Kress, 2016) from the two-dimensional to the three-dimensional case. The idea of the method consists in reformulating Bernoulli's problem as a system of boundary integral equations which are nonlinear with respect to the unknown shape of the free boundary and linear with respect to the boundary values. The system is linearized simultaneously with respect to both unknowns, i.e., it is solved by Newton iterations. In each iteration step the linearized system is solved numerically by a spectrally accurate method. After expressing the Fréchet derivatives as a linear combination of single- and double-layer potentials we obtain a local convergence result on the Newton iterations and illustrate the feasibility of the method by numerical examples. | URI: | http://doi.org/10.1016/j.camwa.2017.06.011 http://hdl.handle.net/11147/6767 |
ISSN: | 0898-1221 |
Appears in Collections: | Mathematics / Matematik Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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