Computer-aided triangulation algorithm for multiply connected domains with concentrated and rarefied nodes (Q2714085)

The article is devoted to describing a computer-aided algorithm for triangulation of arbitrary two-dimensional multiply connected domains. In particular, the main attention is paid to the algorithms for decomposition and triangulation of a piecewise smooth closed boundary contour. The authors use the results by N.~I.~Mil'kova, V.~I.~Sakalo, and A.~A.~Shkurin on constructing triangular finite elements which fill the domain under consideration. The algorithm starts with a given decomposition of the boundary of the domain which adjusts the sizes of one-dimensional and triangular finite elements according to their position in the domain. In the triangulation process, the so-called step function is used and the following function can be considered: NEWLINE\[NEWLINE h(x,y) = h_0 + \sum_{i = 1}^n\frac{h_i - h_0}{1 + (\tilde x_i/A_i)^{N_i} + (\tilde y_i/B_i)^{N_i}}, NEWLINE\]NEWLINE where \(h_0\) is the basic mesh width, \(n\) is the amount of concentrations or rarefications of the mesh, \(h_i\) denotes the mesh width in the \(i\)-center, \(A_i\) and \(B_i\) determine the size of the domain of concentration, \(N_i\) is the exponent of the concentration gradient for a given mesh.NEWLINENEWLINENEWLINEThe algorithm is tested on some samples which represent a ring with two cyclic cuts, a cogged gear and others.