Incomplete Balancing Domain Decomposition for Large scale 3-D non-stationary incompressible flow problems

To solve large scale 3-D non-stationary incompressible flow problems, an algorithm to perform an Incomplete Balancing Domain Decomposition (IBDD) is constructed in this work; as an improvement of the Balancing Domain Decomposition (BDD) method, it reduce the computation cost of the coarse problem by replacing the exact balancing procedure with an inexact balancing procedure; the nonlinear convection term of the Navier-Stokes equation is approximated by a characteristic-curve method, which is advantageous as it renders the matrix for linear equations symmetric, thus enabling the Conjugate Gradient (CG) method to be used together with the Schur complement system of Domain Decomposition Method (DDM); the algorithms are all implemented in parallel by the Hierarchical Domain Decomposition Method (HDDM) system, and the program provides solvability for models of over 10 million degrees of freedom (DOF).