Method of creation of multi-connected area's finite element representation
Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 119-129.

Voir la notice de l'article provenant de la source Math-Net.Ru

Description of method of finite element mesh construction of multi-connected areas has been given in this article. Finite element mesh of the area configuration is described by discrete set, consisting of the number of nodes and elements of the finite element mesh, arranged sets of node coordinates and node numbers on the finite elements. For the proof of a correctness of a method of the solution the appropriate theorems are provided. Adequacy of finite element model of topology of the multi-connected area is shown. Combining subareas is performed on the basis of boundary nodes' coincidence criteria through the establishment of a simple hierarchy of volumes, surfaces, lines and points. Renumbering of nodes is carried out by usage of Frontal Method, where edge nodes are used as starting nodes.
Keywords: method, finite element, mesh, numbering, peak, edge, algorithm, multi-connected, areas.
Mots-clés : arrangement, node, front
@article{MM_2018_30_2_a7,
     author = {A. M. Polatov},
     title = {Method of creation of multi-connected area's finite element representation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {119--129},
     publisher = {mathdoc},
     volume = {30},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2018_30_2_a7/}
}
TY  - JOUR
AU  - A. M. Polatov
TI  - Method of creation of multi-connected area's finite element representation
JO  - Matematičeskoe modelirovanie
PY  - 2018
SP  - 119
EP  - 129
VL  - 30
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2018_30_2_a7/
LA  - ru
ID  - MM_2018_30_2_a7
ER  - 
%0 Journal Article
%A A. M. Polatov
%T Method of creation of multi-connected area's finite element representation
%J Matematičeskoe modelirovanie
%D 2018
%P 119-129
%V 30
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2018_30_2_a7/
%G ru
%F MM_2018_30_2_a7
A. M. Polatov. Method of creation of multi-connected area's finite element representation. Matematičeskoe modelirovanie, Tome 30 (2018) no. 2, pp. 119-129. http://geodesic.mathdoc.fr/item/MM_2018_30_2_a7/

[1] M.P. Galanin, I.A. Shcheglov, “Razrabotka i realizatsiya algoritmov trekhmernoy triangulyatsii slozhnykh prostranstvennykh oblastey: iteratsionnyye metody”, Keldysh Institute preprints, 2006, 009, 32 pp.

[2] M.P. Galanin, I.A. Shcheglov, “Razrabotka i realizatsiya algoritmov trekhmernoy triangulyatsii slozhnykh prostranstvennykh oblastey: pryamyye metody”, Keldysh Institute preprints, 2006, 010, 32 pp.

[3] Kh. A. Kamel', G. K. Eyzenshteyn, “Avtomaticheskoye postroyeniye setki v dvukh- i trekhmernykh sostavnykh oblastyakh. Raschet uprugikh konstruktsiy s ispol'zovaniyem EVM”, Sbornik nauchnykh trudov, v. 2, Sudostroyeniye, L., 1974, 21–35

[4] I.A. Shcheglov, Diskretizatsiia slozhnykh dvumernikh i trekhmernikh oblastei dlia resheniia zadach matematicheskogo modelirovaniia, Avtoreferat dissertatsii ... kand.fiz.-mat. nauk, MGTU im. N. E. Baumana, M., 2010, 16 pp.

[5] S.A. Sukov, “Metody generathii tetraedralnykh setok i ikh programmnie realizarsii”, Keldysh Institute preprints, 2015, 023, 22 pp.

[6] A.A. Kliachin, A.Iu. Belenikina, “Trianguliatsiia prostranstvennikh elementarnikh oblastei”, Vestnik VolGU. Seriia 1. Matematika. Fizika, 2015, no. 4, 6–12

[7] A.M. Polatov, A.Iu. Fedorov, “Algoritm minimizatsii shiriny lenty systemy uravnenii”, Sovremennie informatsionnie tekhnologii v nauke, obrazovanii i praktike, Orenburg, 2007, 103–105

[8] A.I. Sakovich, I.A. Kholmyanskiy, “Minimizatsiya shiriny lenty sistemy uravneniy v metode konechnykh elementov”, Problemy prochnosti, 1981, no. 1, 120–122

[9] Alan George, Joseph W. Liu, Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981, 324 pp. | MR