METHODOLOGY OF VARIATIONAL APPROACH TO QUASI-OR- THOGONAL GRID CONSTRUCTION

G. P. Prokopov
VANT. Ser. Mat. Mod. Fiz. Proc 1998. Вып.1. С. 37-46.

      To obtain grids close to orthogonal ones (quasi-orthogonal grids) the functional regularization is implemented that is equivalent to adding elliptic functionals with quite small weight.
      For providing a grid nondegeneracy the functional discretization is performed similarly to the “variational barrier” technique proposed for the widely used functional representing Dirichlet integral for the inverse mapping.
      The functional minimization using the direct descent technique which doesn’t use the functional gradient permits to avoid numerical integration of Euler equation system (that would be quite bulky) and great difficulties when using numerical techniques such as splitting to solve it.
      The developed algorithm of the descent technique implementation for an arbitrary functional allows to restrict computations by functional calculation on a local pattern including grid nodes (in the case, when the functional integrand expression depends on its first derivatives).