Article
MSC:
31B10,
35J05,
35J15,
35J25,
35J67,
65E05,
65N30,
78-08,
78A20,
78A45 | MR 0973240 | Zbl 0694.65052 | DOI: 10.21136/AM.1988.104324
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Keywords:
3-dimensional potential problem; Ritz-Galerkin approximation; convergence; diffraction; nonlocal boundary condition; finite elements
3-dimensional potential problem; Ritz-Galerkin approximation; convergence; diffraction; nonlocal boundary condition; finite elements
Summary:
Assuming an incident wave to be a field source, we calculate the field potential in a neighborhood of an inhomogeneous body. This problem which has been formulated in $\bold R^3$can be reduced to a bounded domain. Namely, a boundary condition for the potential is formulated on a sphere. Then the potential satisfies a well posed boundary value problem in a ball containing the body. A numerical approximation is suggested and its convergence is analyzed.
References:
[1] V. Drápalík V. Janovský: On a potential problem with incident wave as a field source. Aplikace matematiky 33 (1988), 443-455 MR 0973239
[2] J. L. Lions E. Magenes: Problèmes aux limites non homogènes et applications. Dunod, Paris 1968.
[3] G. C. Hsiao P. Kopp W. L. Wendland: A Galerkin collocation method for some integral equations of the first kind. Computing 25 (1980), 89-130. DOI 10.1007/BF02259638 | MR 0620387
[4] G. C. Hsiao W. L. Wendland: A finite element method for some integral equations of the first kind. J. Math. Appl. Anal. 58 (1977), 449-481. DOI 10.1016/0022-247X(77)90186-X | MR 0461963
[5] C. Johnson J. C. Nedelec: On the coupling of boundary integral and finite element methods. Math. Соmр. 35 (1980), 1063-1079. MR 0583487
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