A FACTORIZATION-RELATED METHOD FOR ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS WITH ITERATIVE IMPROVEMENT

We consider a method for solving elliptic boundary-value problems. The method arises from a finite-difference discretization which has one form in the interior region, but is modified near the boundary. This permits the problem to be solved in terms of sparse upper and lower triangular matrices. The result of this direct method is then improved by an iterative technique, which is further enhanced by a multigrid-type process.For the type of problems we consider here, the total combined method requires only O(N2) time and O(N2) space to compute the solution of a system of N × N mesh points to good accuracy. The method is applied to a case where normal discretization leads to a matrix that is not positive definite. © 1990 Oxford University Press.