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Zbl 0851.65074
Ben-Porat, Gil; Givoli, Dan
Solution of unbounded domain problems using elliptic artificial boundaries. (English)
[J] Commun. Numer. Methods Eng. 11, No.9, 735-741 (1995). ISSN 1069-8299; ISSN 1099-0887/e

In order to solve the two-dimensional Laplace and Helmholtz equations in an unbounded domain, the authors propose the introduction of an artificial boundary with exact conditions on it. While in previous papers this problem has been dealt with by choosing circular boundaries, in the present one ellipses are used instead, because they can enclose slender obstacles in a more adapted way. Accordingly, the introduction of elliptic coordinates produces appropriate eigenfunctions for each of the equations; for the explicit finite element calculation the authors refer to the circular boundary case.\par The performance of the method is demonstrated with the two-dimensional potential flow around an aerfoil and with the time harmonic waves radiated from a rigid circular obstacle; in the first example, comparison with the numerical solution obtained by a far-field flow condition imposed on a rectangular boundary shows the much better accuracy that can be obtained with the approach proposed in the paper.
[J.P.Milaszewicz (Buenos Aires)]

MSC 2000:: *65N30 Finite numerical methods (BVP of PDE)
76B10 Free-streamline theory and appl.
35J05 Laplace equation, etc.

Keywords: Laplace equation; Helmholtz equations; unbounded domain; artificial boundary; elliptic coordinates; finite element; performance; potential flow around an aerfoil; time harmonic waves

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