PLANE DOMAIN TRIANGULATION WITH DIRICHLET PROBLEM SOLUTION
BY THE METHOD OF FINITE ELEMENTS IN GALERKIN FORM

Polyansky Dmitry Yuryevich, Candidate of engineering sciences, associate professor, rector of Vladimir polytechnic college, adm@polcol.elcom.ru

539.3

The author has solved a new problem of triangulation of sufficiently regular bounded flat domain. The domain is represented by a combination of nonintersecting convex curvilinear subdomains with the number of angles from 3 to 6. Each subdomain is given a corresponding equivalent analog - an equilateral triangle or a convex polygon generated by it. The equivalent analog is transformed into a discrete one consisting of equilateral triangles. A conformal image of the discrete analog on the domain under analysis is made by the FEA solution in Galyorkin form of the boundary value Dirichlet problem using Laplacian. The result of the imaging is a discrete model of the domain under investigation with the triangular elements being close to equilateral.

triangulation, method of final elements, conformal image, boundary value Dirichlet problem.