Evaluation of the residual vector in global element calculations

摘要

The defining equations for the global element method [5], applied to the solution of (linear or nonlinear) elliptic partial differential equations, are most efficiently solved using an iterative scheme. It has been shown previously [6] that for a calculation in two dimensions, the operation count of such a scheme is O(MN4) where M is the number of elements and N the size of the expansion used to approximate the solution in each element. This operation count results partly from the need to multiply an MN2 vector by an MN2 × MN2 matrix to form the residual vector at each iteration. We demonstrate here how the residual can be computed with the improved operation count of O(MN2 ln N): an additional advantage of the new scheme is that the full diagonal blocks of the coefficient matrix need not be assembled.