Incorporation of multipoint constraints into the balancing domain decomposition method and its parallel implementation

The domain decomposition method (DDM) is a major solution algorithm that is used to parallelize the finite element method. In the case of implicit structural analysis using the DDM, the substructuring-based iterative linear solver is a powerful tool when an effective preconditioner such as the balancing domain decomposition (BDD) method is used. In the present study, a method by which to incorporate a set of linear multipoint constraints (MPC) into the BDD method is proposed. In this method, when an MPC is enforced on the internal degrees of freedom (DOFs) in some subdomains, the DOFs are converted into interface DOFs, that is, all of the DOFs constrained by MPCs become interface DOFs. Then, the interface problem with the set of MPCs for the interface DOFs is solved by the conjugate projected gradient method. In order to combine the above procedure with the preconditioner used in the BDD method, the effect of the MPCs for the interface DOFs is also imposed on the coarse grid problem of the BDD method using the penalty method. A parallel implementation of the present method is also described. Some illustrative examples are solved and good convergence and parallel performance of the present method are demonstrated. Copyright q 2006 John Wiley & Sons, Ltd.