73 research outputs found
The INTERNODES method for applications in contact mechanics and dedicated preconditioning techniques
The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems
Fast Nonsymmetric Iterations and Preconditioning for Navier-Stokes Equations
Discretization and linearization of the steady-state Navier-Stokes equations
gives rise to a nonsymmetric indefinite linear system of equations. In this
paper, we introduce preconditioning techniques for such systems with the
property that the eigenvalues of the preconditioned matrices are bounded
independently of the mesh size used in the discretization. We confirm and
supplement these analytic results with a series of numerical experiments
indicating that Krylov subspace iterative methods for nonsymmetric systems
display rates of convergence that are independent of the mesh parameter.
In addition, we show that preconditioning costs can be kept small by
using iterative methods for some intermediate steps performed by the
preconditioner.
(Also cross-referenced as UMIACS-TR-94-66
Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions
Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups
Preconditioners for iterative solutions of large-scale linear systems arising from Biot's consolidation equations
Ph.DDOCTOR OF PHILOSOPH
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