The Fast Numerical-Solution Of Very Large Elliptic Difference Schemes

Let Lkvk = gk be a system of difference equations discretizing an elliptic boundary value problem. Assume the system to be “very large”, that means that the number of unknowns exceeds the capacity of storage. We present a method for solving the problem with much less storage requirement. For two-dimensional problems the size of the needed storage decreases from O(h−2) to (or even O(h−5/4)). The computational work increases only by a factor about six. The technique can be generalized to nonlinear problems. The algorithm is also useful for computers with a small number of parallel processors.