Super Element Method of Arbitrary Order in the Problems of Filtration

This work presents an extension of the Super Element Method (SEM, Phedorenko R.P.) to the case of arbitrary order, different in each coordinate direction, on the example of the 2D elliptical linear equation. Also we consider two ways of SEM application for the linear parabolic equation. Some elliptic filtration problems solving by SEM and containing a well and a zone of low permeability are considered as illustration. For such problems a method of local grid subdividing near the well is suggested. The constructed grid is orthogonal, matches rectangular and polar grids, and corresponds to the flow geometry near the well. SEM has some advantages: it naturally gives the solution of the problem of averaging (homogenization) of the permeability values on subregions and allows effective parallelization of the computational process. This work also contains some results on comparison of the two numerical methods for the solution of linear algebraic equation systems: the Multigrid method (MG5 code by Phedorenko R.P.) and the Gauss incomplete factorization method with iterations (T92 code by Turchaninov V.I.).