Exact interpolation scheme with approximation vector used as a column of the prolongator

Abstract

SummaryOur method is a kind of exact interpolation scheme by Achi Brandt et al. In the exact interpolation scheme, for x being the fine‐level approximation of the solution, the coarse‐space V = V(x) is constructed so that x satisfies x∈V. We achieve it simply by adding the vector x as a first column of the prolongator. (The columns of the prolongator P form a computationally relevant basis of the coarse‐space V = Range(P).) The advantages of this construction become obvious when solving non‐linear problems. The cost of enriching the coarse‐space V by the current approximation x is a single dense column of the prolongator that has to be updated each iteration. Our method can be used for multilevel acceleration of virtually any iterative method used for solving both linear and non‐linear systems. Copyright © 2015 John Wiley & Sons, Ltd.