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The nonoverlapping domain decomposition (DD) method allows to store vectors as accumulated or as distributed (each process stores a part of that value) vectors. The case of distributed stored matrices is fully investigated, whereas the use of accumulated matrices is not customary in the DD community. This paper is concerned with the accumulated matrices and investigates conditions under which matrix-by-vector multiplications can be realized. Especially, we derive restrictions on the matrix shape and the nite element (FE) mesh. As a new result, the special structure of these admissible accumulated matrices leads directly to global incomplete factorizations as preconditioners in CG-like methods. Also, the well-known DD preconditioners t into the general framework of the matrix-by-vector operations presented.