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).
Santrauka. Straipsnyje nagrinėjamas ciklinio tipo tikslios simetrijos sritys. R – funkcijų metodas taikomas sudarant simetrinių objektų kontūrų lygtis. Šis metodas, kombinuojant jį su Ritz‘o metodu, panaudotas sprendžiant Laplaso lygties Dirichle kraštinį uždavinį sudėtingoje simetrinėje srityje. Uždavinys aprašo elektrostatinio lauko, gaunamo susikertant magnetinių laukų sistemai, potencialo pasiskirstymą, t. y., jis modeliuoja reversinės konstrukcijos cilindrinį magnetroną. Šis uždavinys realizuotas skaitiškai kompiuterinės programos POLYE pagalba.
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
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