Previous |  Up |  Next


quasilinear elliptic equation; domain decomposition method; natural integral equation
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.
[1] Du, Q., Yu, D.: A domain decomposition method based on natural boundary reduction for nonlinear time-dependent exterior wave problems. Computing 68 (2002), 111-129. DOI 10.1007/s00607-001-1432-y | MR 1901139 | Zbl 1004.65098
[2] Du, Q., Yu, D.: Dirichlet-Neumann alternating algorithm based on the natural boundary reduction for time-dependent problems over an unbounded domain. Appl. Numer. Math. 44 (2003), 471-486. DOI 10.1016/S0168-9274(02)00188-5 | MR 1957689 | Zbl 1013.65102
[3] Du, Q., Zhang, M.: A non-overlapping domain decomposition algorithm based on the natural boundary reduction for wave equations in an unbounded domain. Numer. Math., J. Chin. Univ. 13 (2004), 121-132. MR 2156269 | Zbl 1075.65121
[4] Feng, K.: Finite element method and natural boundary reduction. Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, Z. Ciesielski et al. PWN-Polish Scientific Publishers Warszawa; North-Holland, Amsterdam (1984), 1439-1453. MR 0804790 | Zbl 0569.65076
[5] Han, H., Huang, Z., Yin, D.: Exact artificial boundary conditions for quasilinear elliptic equations in unbounded domains. Commun. Math. Sci. 6 (2008), 71-82. DOI 10.4310/CMS.2008.v6.n1.a4 | MR 2397998 | Zbl 1168.65412
[6] Hlaváček, I.: A note on the Neumann problem for a quasilinear elliptic problem of a nonmonotone type. J. Math. Anal. Appl. 211 (1997), 365-369. DOI 10.1006/jmaa.1997.5447 | MR 1460177 | Zbl 0876.35041
[7] Hlaváček, I., Křížek, M., Malý, J.: On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type. J. Math. Anal. Appl. 184 (1994), 168-189. DOI 10.1006/jmaa.1994.1192 | MR 1275952
[8] Ingham, D. B., Kelmanson, M. A.: Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems. Lecture Notes in Engineering 7 Springer, Berlin (1984). DOI 10.1007/978-3-642-82330-5 | MR 0759537 | Zbl 0553.76001
[9] Liu, D., Yu, D.: A FEM-BEM formulation for an exterior quasilinear elliptic problem in the plane. J. Comput. Math. 26 (2008), 378-389. MR 2421888 | Zbl 1174.65049
[10] Meddahi, S., González, M., Pérez, P.: On a FEM-BEM formulation for an exterior quasilinear problem in the plane. SIAM J. Numer. Anal. 37 (2000), 1820-1837. DOI 10.1137/S0036142998335364 | MR 1766849
[11] Yang, M., Du, Q.: A Schwarz alternating algorithm for elliptic boundary value problems in an infinite domain with a concave angle. Appl. Math. Comput. 159 (2004), 199-220. DOI 10.1016/j.amc.2003.10.042 | MR 2094966 | Zbl 1071.65171
[12] Yu, D.: Domain decomposition methods for unbounded domains. Domain Decomposition Methods in Sciences and Engineering (Beijing, 1995) R. Glowinski et al. Wiley Chichester 125-132 (1997). MR 1943455
[13] Yu, D.: Natural Boundary Integral Method and its Applications. Translated from the 1993 Chinese original. Mathematics and its Applications 539 Kluwer Academic Publishers, Dordrecht (2002); Science Press Beijing, Beijing MR 1961132 | Zbl 1028.65129
[14] Zhu, W., Huang, H. Y.: Non-overlapping domain decomposition method for an anisotropic elliptic problem in an exterior domain. Chinese J. Numer. Math. Appl. 26 (2004), 87-101. MR 2087218
Partner of
EuDML logo