Abstract
This paper is devoted to developing constructive methods of the theory of R-functions. It gives the first discussion of methods of constructing the equations of loci with symmetry of translation type for duplicated domains not separated by lines and with point symmetry of cyclic type for regions both possessing and lacking axial symmetry. The possible applications are illustrated by numerous examples carried out using the POLE system, including solutions of boundary-value problems involving the influence of cyclically located circular and star-shaped insulators on an electric field.
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Literature Cited
L. V. Kantorovich and V. I. Krylov,Approximate Methods of Higher Analysis [in Russian], Gostekhizdat, Moscow (1950).
V. L. Rvachev,The Theory of R-Functions and Some of its Applications [in Russian], Naukova Dumka, Kiev (1982).
V. L. Rvachev and L. V. Kurpa,R-Functions in Problems of the Theory of Plates [in Russian], Naukova Dumka, Kiev (1987).
V. L. Rvachev and N. S. Sinekop,The R-Function, Method in Problems of the Theory of Elasticity and Plasticity [in Russian], Naukova Dumka, Kiev (1990).
V. L. Rvachev and T. I. Sheiko, “R-functions in boundary-value problems in mechanics,”Appl. Mech. Rev.,48, No. 4, 151–188 (1995).
V. L. Rvachev, T. I. Sheiko, V. Shapiro, and J. J. Uicker, “Implicit function modeling of solidification in metal casting, Technical Report SAL 1996-4, Spatial Automation Laboratory, University of Wisconsin, October 1996, pp. 1–14.
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Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 146–159.
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Rvachev, V.L., Sheiko, T.I. & Shapiro, V. TheR-function method in boundary-value problems with geometric and physical symmetry. J Math Sci 97, 3888–3899 (1999). https://doi.org/10.1007/BF02364929
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DOI: https://doi.org/10.1007/BF02364929