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.
@article{104324,
author = {Vladim\'\i r Dr\'apal\'\i k and Vladim\'\i r Janovsk\'y},
title = {Numerical treatment of 3-dimensional potential problem},
journal = {Applications of Mathematics},
volume = {33},
year = {1988},
pages = {456-469},
zbl = {0694.65052},
mrnumber = {0973240},
language = {en},
url = {http://dml.mathdoc.fr/item/104324}
}
Drápalík, Vladimír; Janovský, Vladimír. Numerical treatment of 3-dimensional potential problem. Applications of Mathematics, Tome 33 (1988) pp. 456-469. http://gdmltest.u-ga.fr/item/104324/
On a potential problem with incident wave as a field source, Aplikace matematiky 33 (1988), 443-455 (1988) | MR 0973239
Problèmes aux limites non homogènes et applications, Dunod, Paris 1968. (1968)
A Galerkin collocation method for some integral equations of the first kind, Computing 25 (1980), 89-130. (1980) | Article | MR 0620387
A finite element method for some integral equations of the first kind, J. Math. Appl. Anal. 58 (1977), 449-481. (1977) | Article | MR 0461963
On the coupling of boundary integral and finite element methods, Math. Соmр. 35 (1980), 1063-1079. (1980) | MR 0583487