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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
Issue Date: Dec-2017
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.
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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