Abstract
We propose a method of numerical conformai mapping of periodic structure domains onto periodic parallel slit domains. In the method presented here, the mapping problem is reduced to a Dirichlet one for a pair of conjugate harmonic functions with a periodic boundary condition. We modify the charge simulation method for solving periodic boundary value problem and apply it to our mapping problem. Some numerical examples show that our method is efficient. We also show an application of our method to the analysis of potential flow past obstacles in a periodic array.
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K. Amano, Y. Shibuya, M. Tsuchie and M. Sugihara, Numerical conformai mapping onto the parallel slit domains by the charge simulation method (in Japanese). Trans. Japan. SIAM,6, No. 4 (1996), 353–371.
K. Amano, A charge simulation method for numerical conformai mapping onto circular and radial slit domains. SIAM J. Sci. Comput.,19, No. 4 (1998), 1169–1187.
K. Amano, D. Okano, H. Ogata, H. Shimohira and M. Sugihara, A systematic scheme of numerical conformai mappings of unbounded multiply-connected domains by the charge simulation method (in Japanese). IPSJ J.,42, No. 3 (2001), 385–395.
K. Amano, D. Okano, H. Shimohira, T. Okamoto and Y. Igaue, Potential flow analysis by the numerical conformai mapping. Information,3, No. 1 (2000), 73–88.
G.K. Batchelor, An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, 1967.
H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their applications to viscous flow past a cubic array of spheres. J. Fluid Mech.,5 (1959), 317–328.
P. Henrici, Applied and Computational Complex Analysis,3. Wiley, New York, 1986.
I. Imai, Conformai Mapping and Its Applications (in Japanese). Iwanami Shoten, Tokyo, 1979.
P.K. Kythe, Computational Conformai Mapping. Birkhäuser, Boston, 1998.
Z. Nehari, Comformal Mapping. McGraw-Hill, New York, 1952; Dover, New York, 1975.
L.N. Trefethen (ed.), Numerical Conformai Mapping. North-Holland, Amsterdam, 1986; J. Comput. Appl. Math.,14, Nos.1 & 2 (1986).
E.T. Whittaker and G.N. Watson, A Course of Modern Analysis. (4th Ed.). Cambridge University Press, Cambridge, 1927.
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Ogata, H., Okano, D. & Amano, K. Numerical conformai mapping of periodic structure domains. Japan J. Indust. Appl. Math. 19, 257–275 (2002). https://doi.org/10.1007/BF03167456
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DOI: https://doi.org/10.1007/BF03167456