Geodesic
Method of boundary integral equations as applied to the numerical solution of the three-dimensional Dirichlet problem for the laplace equation in a piecewise homogeneous medium
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1197-1206

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A Dirichlet problem is considered in a three-dimensional domain filled with a piecewise homogeneous medium. The uniqueness of its solution is proved. A system of Fredholm boundary integral equations of the second kind is constructed using the method of surface potentials, and a system of boundary integral equations of the first kind is derived directly from Green's identity. A technique for the numerical solution of integral equations is proposed, and results of numerical experiments are presented. 
@article{ZVMMF_2009_49_7_a6,
     author = {E. V. Zakharov and A. V. Kalinin},
     title = {Method of boundary integral equations as applied to the numerical solution of the three-dimensional {Dirichlet} problem for the laplace equation in a~piecewise homogeneous medium},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {49},
     number = {7},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a6/}
}
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E. V. Zakharov; A. V. Kalinin. Method of boundary integral equations as applied to the numerical solution of the three-dimensional Dirichlet problem for the laplace equation in a piecewise homogeneous medium. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1197-1206. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a6/