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The R‐functions method in the boundary value problem for a complex domain possessing the symmetry

    Yu. S. Semerich Affiliation

Abstract


This paper considers a case of the punctual symmetry of cyclic type and application of the R‐functions method in building equations of the boundaries for symmetric objects. The R‐functions method combined with the Ritz method is used for solving the Laplace equation in the complex symmetric domain. The problem is described for calculating an electrostatic field in the system with crossed fields (the cylindrical magnetron of reversed construction).


R-funkcijų metodas kraštiniam uždaviniui sudėtingose srityse, turinčiose simetriją


Santrauka



Staipsnyje nagrinejamas ciklinio tipo tikslios simetrijos sritys. R ‐ funkciju metodas taikomas sudarant simetriniu objektu kontūru lygtis. Šis metodas, kombinuojant ji su Ritz'o metodu, panaudotas sprendžiant Laplaso lygties Dirichle kraštini uždavini sudetingoje simetrineje srityje. Uždavinys aprašo elektrostatinio lauko, gaunamo susikertant magnetiniu lauku sistemai, potencialo pasiskirstyma, t.y., jis modeliuoja reversines konstrukcijos cilindrini magnetrona. Šis uždavinys realizuotas skaitiškai kompiuterines programos POLYE pagalba.


First Published Online: 14 Oct 2010

Keyword : The R‐functions method, symmetry, the Laplace equation, cylindrical magnetron, general structure of solution

How to Cite
Semerich, Y. S. (2003). The R‐functions method in the boundary value problem for a complex domain possessing the symmetry. Mathematical Modelling and Analysis, 8(1), 77-86. https://doi.org/10.3846/13926292.2003.9637212
Published in Issue
Mar 31, 2003
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