Composite grid method for hybrid systems Original Research Article

A composite grid method is developed for solving symmetric indefinite linear systems arising from the three-field hybrid variational principle, which weakly enforces compatability and traction continuity conditions between independently modeled substructures. The new solution approach decomposes the hybrid system into a hierarchical global-local problem consisting of a positive definite global problem and an indefinite local system that are derived using minimization on the subspace and the stationarity principle, respectively. An innovative transformation of the indefinite local problem into an equivalent symmetric positive definite system makes the solution of the local problem possible either by a direct solver without pivoting or by a preconditioned iterative method. Alternative semi-iterative solution procedures for the case when auxiliary coarse grid is not available, are also developed. This includes a multigrid-like scheme that uses a mathematical model based on the collocation formulation as the auxiliary grid. Numerical performance studies for two-dimensional plane stress and shell problems are carried out to test the usefulness of the proposed procedures.