Multispace and Multilevel BDDC

BDDC method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl

Finite element pressure stabilizations for incompressible flow problems

Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis

Experimental-based modeling of a support structure as part of a full system model

Structural dynamic systems are often attached to a support structure to simulate proper boundary conditions during testing. In some cases the support structure is fairly simple and can be modeled by discrete springs and dampers. In other cases the desired test conditions necessitate the use of a support structural that introduces dynamics of its own. For such cases a more complex structural dynamic model is required to simulate the response of the full combined system. In this paper experimental frequency response functions, admittance function modeling concepts, and least squares reductions are used to develop a support structure model including both translational and rotational degrees of freedom at an attachment location. Subsequently, the modes of the support structure are estimated, and a NASTRAN model is created for attachment to the tested system