Key points are not available for this paper at this time.
The subject of this paper is the application of the multi-grid method to the solution of \ - (D (x, y) U (x, y) ) + (x, y) U (x, y) = f (x, y) \ in a bounded region of R² where D is positive and D, , and f are allowed to be discontinuous across internal boundaries of. The emphasis is on discontinuities of orders of magnitude in D, when special techniques must be applied to restore the multi-grid method to good efficiency. These techniques are based on the continuity of D U across. Two basic methods are derived, one in which the approximating finite difference operators on coarser grids are five point operators (assuming the finite difference operator on the finest grid is a five point one) and one in which they are nine point operators.
Alcouffe et al. (Tue,) studied this question.