Calculation of Quasi-Orthogonal Grid by Minimization of the Variational Functionals

A general form of a variational functional is proposed. Minimum of this functional is attained on orthogonal grid. A regularization procedure is used, because of instability in its numerical implementation. These grids are called quasi-orthogonal. To provide a grid to be nondegenerate, a discretization of functional similar to known 'variational barrier method' is used. A method, which does not use the gradient of the functional, is employed for minimization of the functional. The algorithm allows to use local procedures for computation the values of the functional on local stencil. The possibility of this approach is illustrated by methodical tests.