Analytical modelling of perforated geometrical domains by the R-functions

This paper deals with the construction of boundary equations for geometric domains with perforation. Different types of perforated geometric domains are considered. The R-functions method for analytical modelling of perforated geometrical domains is used. For all constructed equations, function plots are obtained

The construction of loci with a cyclical symmetry by the R‐functions

This paper deals with the development of the R‐functions method for construction of equations describing a boundary of locus in the case of cyclical symmetry. The proposed method is based on transformations of coordinates and canonical locus. Darbe pateiktas būdas, kaip pritaikyti R‐funkciju metoda taip vadinamu ciklines simetrijos sričiu kontūru lygtims sudaryti. Pasiūlytasis metodas pagristas loordinačiu transformavimu, pasinaudojant kanoniniu hodografu. First Published Online: 14 Oct 201

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

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 201