Juxtaposition-based domain decomposition requires complicated pre-processing and communications of pre-consolidated data, and is restricted to field problems. In this paper, we propose a superposition-based domain decomposition parallelization, which employs element-by-element construction, processor-level assembling, and condensed random data structure. Superposition-based parallelization shows great flexibility in partitioning the computational domains, communicates more consolidated data, and can be applied beyond field problems. Moreover, superposition-based parallelization can, as an option, follow the same numerical process as its serial counterpart to produce digit-by-digit identically the same result, which makes code development and debugging much easier. Solving large scale indefinite systems continues to pose as a challenging issue for incompressible flows. In this paper, we propose the discrete operator splitting (DOS) technique to break the original ill-natured large indefinite system into two smaller well-natured definite systems coupled through source terms. The underpinning idea of the technique is to seamlessly combine the splitting and iterations together. Equipped with the parallelization and DOS, we present in details the superposition-based parallel discrete operator splitting finite element method and apply it to incompressible Navier-Stokes flows. Backward-facing step flow, cavity flow, and pipe flow are simulated to demonstrate the success of the method. (C) 2009 Elsevier Ltd. All rights reserved.