Abstract
In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze its convergence. Moreover, the convergence rate is obtained in detail for a typical domain. Finally, some numerical examples are presented to illustrate the feasibility of the method.
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This work is supported by the National Natural Science Foundation of China, contact/grant number 11371198, the Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems contract/grant number 201305, and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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Liu, B., Du, Q. Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem. Appl Math 59, 285–301 (2014). https://doi.org/10.1007/s10492-014-0055-5
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DOI: https://doi.org/10.1007/s10492-014-0055-5