Paper Info
Title
Nonlinear integral equations for Bernoulli's free boundary value problem in three dimensions.
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.
Year
DOI
Venue
2017
10.1016/j.camwa.2017.06.011
Computers & Mathematics with Applications
Keywords
Field
DocType
Free boundary,Laplace equation,Boundary integral equation
Boundary knot method,Boundary value problem,Mathematical optimization,Robin boundary condition,Mathematical analysis,Free boundary problem,Local convergence,Singular boundary method,Neumann boundary condition,Mathematics,Mixed boundary condition
Journal
Volume
Issue
ISSN
74
11
0898-1221
Citations 
PageRank 
References 
0
0.34
3
Authors
2
Name
Order
Citations
PageRank
Olha Ivanyshyn1102.27
David Colton23315.98