Dual-Primal FETI Method
نویسندگان
چکیده
The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioner was shown to be numerically scalable for second order elasticity problems while the two level FETI method was designed to be numerically scalable for fourth order elasticity problems (see [FR94, Far91b, Far91a, FR91, FR92, FM98, Rou95]). The second level coarse grid is an enriched version of the original one level FETI method with coarse grid. The coarse problem is enriched by enforcing transverse displacements to be continuous at the corner points. This coarse problem grows linearly with the number of subdomains. Current implementations use a direct solution method to solve this coarse problem. However, the current implementation gives rise to a full matrix system. This full matrix can lead to increased storage requirements especially if working within a distributed memory environment. Also, the factorization and subsequent forward/backward substitutions of the second level coarse problem becomes the dominant factor in solving the global problem as the number of subdomains becomes large (Ns > 1000). We introduce an alternative formulation of the two level coarse problem that leads to a sparse system better suited for a direct method. Then we show extensions to the alternate formulation that allow optional admissible constraints to be added to improve convergence. Lastly, we report on the numerical performance, parallel efficiency, memory requirements, and overall CPU time as compared to the classical two level FETI on some large scale fourth order elasticity problems.
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