In this work we analyse a method to construct numerically efficient and computationally cheap sparse approximations of some of the matrix blocks arising in the block-factorized preconditioners for matrices with a two-bytwo block structure. The matrices arise from finite element discretizations of partial differential equations. We consider scalar elliptic problems, however the approach is appropriate also for other types of problems such as parabolic problems or systems of equations. The technique is applicable for both selfadjoint and non-selfadjoint problems, in two as well as in three space dimensions. We analyse in detail the two-dimensional case and provide extensive numerical evidence for the efficiency of the proposed matrix approximations, both serial and parallel. Two-and three-dimensional tests are included.Keywords Sparse approximate inverses · Finite element method · Element-by-element technique · Block preconditioners Mathematics Subject Classifications (2010) 65F08 · 65F10 · 65F50 · 65M60 Communicated by
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.