Numerical method of quasi-isometric parametrization for two-dimensional curvilinear domains

A method for constructing a quasi-isometric parametrization of a plane curvilinear quadrilateral is described. The parametrization is defined using a generalized Dirichlet variational functional. Based on its minimization, an algorithm for generating grids that implement a quasi-isometric parametrization of quadrilaterals with curved, but sufficiently smooth boundaries is developed. Primary attention is given to the numerical features of the proposed approach.