| The Finite Element Tearing and Interconnecting (FETI) algorithms are numerically scalable iterative domain decomposition methods for solving systems of equations generated from the finite element discretization of second- or fourth-order elasticity problems. These methods have been substantially improved over the last ten years and recently shown parallel scalability up to one thousand processors.; The purpose of this thesis is to present and investigate a dual-primal FETI method, which addresses some of the critical issues related to the original FETI methods. These critical issues involve the accurate computation of the local rigid body modes, the cost and size of the FETI coarse problems with respect to fourth-order elasticity problems, and the overall robustness and versatility of the equation solver. These improvements due to the dual-primal FETI formulation are especially beneficial when implemented on massively parallel distributed memory computers such as the Accelerated Strategic Computing Initiative (ASCI) Red Option supercomputer.; Numerical results will be shown detailing scalability with respect to the mesh size, subdomain size, and the number of elements per subdomain for both second- and fourth-order elasticity problems. Parallel scalability will be reported for various large scale realistic problems on a SGI Origin 2000 and the ASCI Red option massively parallel supercomputer. Lastly, results from linear dynamics, eigenvalue analysis and geometrically non-linear static problems will be shown highlighting the benefits of FETI methods for solving large-scale problems with multiple right hand sides. |
