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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     pages = {1197--1206},
     year = {2009},
     volume = {49},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a6/}
}
TY  - JOUR
AU  - E. V. Zakharov
AU  - A. V. Kalinin
TI  - 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
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 1197
EP  - 1206
VL  - 49
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a6/
LA  - ru
ID  - ZVMMF_2009_49_7_a6
ER  - 
%0 Journal Article
%A E. V. Zakharov
%A A. V. Kalinin
%T 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
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 1197-1206
%V 49
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a6/
%G ru
%F ZVMMF_2009_49_7_a6
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/

[1] Grinberg G. A., Izbrannye voprosy matematicheskoi teorii elektricheskikh i magnitnykh yavlenii, Izd-vo AN SSSR, M., 1948

[2] Bursian V. R., Teoriya elektromagnitnykh polei, primenyaemykh v elektrorazvedke, Nedra, L., 1972

[3] Dmitriev V. I., Zakharov E. V., “Metod rascheta polya postoyannogo toka v neodnorodnykh provodyaschikh sredakh”, Vychisl. metody i programmirovanie, 20, 1973, 175–185

[4] Tozoni O. V., Maergoiz I. D., Raschet trekhmernykh elektromagnitnykh polei, Tekhnika, Kiev, 1974

[5] MacLeod R. S., Brooks D. H., “Recent progress in inverse problems in electrocardiology”, IEEE Engng in Med. Bio. Bag., 17:1 (1998), 73–83 | DOI

[6] Efimov I. P., Sembelashvili A. T., Nikolskii V. H., “Progress v izuchenii mekhanizmov elektricheskoi stimulyatsii serdtsa”, Vestn. aritmologii, 26 (2002), 91–96

[7] Saulnier G. J., Blue R. S., Newell J. C. et al., “Electrical impedance tomography”, IEEE Signal Proc. Magazine, 18:6 (2001), 31–43 | DOI | MR

[8] Dmitriev V. I., Zakharov E. B., “O chislennom reshenii nekotorykh integralnykh uravnenii Fredgolma 1-go roda”, Vychisl. metody i programmirovanie, 10, 1968, 49–54 | MR

[9] Smagin S. I., “Chislennoe reshenie integralnogo uravneniya I roda so slaboi osobennostyu dlya plotnosti potentsiala prostogo sloya”, Zh. vychisl. matem. i matem. fiz., 28:11 (1988), 1663–1673 | MR

[10] Smagin S. I., “Chislennoe reshenie integralnogo uravneniya 1-go roda so slaboi osobennostyu na zamknutoi poverkhnosti”, Dokl. AN SSSR, 303:5 (1988), 1048–1051

[11] Brebbiya K., Telles Zh., Vroubel L., Metody granichnykh elementov, Mir, M., 1987 | MR

[12] Golnik E. R., Vdovichenko A. A., Uspekhov A. A., “Postroenie i primenenie preprotsessora generatsii, upravleniya kachestvom i optimizatsii setok triangulyatsii kontaktnykh sistem”, Informatsionnye tekhnologii, 2004, no. 4, 2–10

[13] Landau L. D., Lifshits E. M., Teoreticheskaya fizika. T. 8. Elektrodinamika sploshnykh sred, Fizmatlit, M., 2003