A bi-partitioned iterative algorithm for solving linear systems arising from incompressible flow problems

摘要: Abstract A novel iterative algorithm, called the bi-partitioned method, is introduced for efficiently solving system of linear equations that arises from stabilized finite element formulation Navier–Stokes equations. The algorithm a Krylov subspace method designed matrix with separated momentum and continuity blocks. This structure allows formation Schur complement to separately solve velocity pressure unknowns. Hence, can also be applied problems similar , involving complement. Two separate spaces are constructed iteratively solution candidates optimally combined produce final solution. calculates given tolerance, regardless approximation made in construction proposed analyzed compared generalized minimal residual (GMRES) using two incompressible-flow one fluid–structure-interaction example, exhibiting up an order magnitude improvement simulation cost while maintaining excellent stability.