On compatible transfer operators in nonsymmetric algebraic multigrid (Q6577447)

This paper develops analytic formulae on constructing ``compatible'' transfer operators in nonsymmetric algebraic multigrid such that for coarse-grid correction \(\| \Pi \| = 1\) in some standard matrix-induced norm. The work is organized as follows. Section 1 is a Background. The development of background theory on projections is given in Section 2. In Section 3, the necessary and sufficient conditions are developed. Finally, further observations are provided in Section 4, including observations on the compatibility of relaxation with nonorthogonal projections in approximate ideal restriction.