Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis

We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes problem have been proposed, often the analysis was restricted to single-patch domains. We focus on one of the simplest approaches, the isogeometric Taylor--Hood element. We show how stability results for single-patch domains can be carried over to multi-patch domains. While this is possible, the stability strongly depends on the shape of the geometry. We construct a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solver that does not suffer from that effect. We give a convergence analysis and provide numerical tests

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth

Computational Engineering

The focus of this Computational Engineering Workshop was on the mathematical foundation of state-of-the-art and emerging finite element methods in engineering analysis. The 52 participants included mathematicians and engineers with shared interest on discontinuous Galerkin or Petrov-Galerkin methods and other generalized nonconforming or mixed finite element methods

Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization

The workshop has brought together experts in the broad field of partial differential equations with highly heterogeneous coefficients. Analysts and computational and applied mathematicians have shared results and ideas on a topic of considerable interest both from the theoretical and applied viewpoints. A characteristic feature of the workshop has been to encourage discussions on the theoretical as well as numerical challenges in the field, both from the point of view of deterministic as well as stochastic modeling of the heterogeneities

Parallel finite element modeling of the hydrodynamics in agitated tanks

Mixing in the transition flow regime -- Technology to mix in transition flow regime -- Methods to characterize mixing hydrodynamics -- Challenges to numerically model transition flow regime in agited tanks -- Transition flow regime in agitated tanks -- Parallel computing -- Numerical modeling of the agitators motion -- Overall methodological approach -- Computational resources -- Program development strategy -- Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers -- Parallel numerical model -- Parallel implementation -- Three-dimensional benchmark cases -- A parallel finite element sliding mesh technique for the Navier-Stokes equation -- Numerical method -- Parallel implementation -- Numerical examples -- Parallel performance -- Finite element modeling of the laminar and transition flow of the Superblend dual shaft coaxial mixer on parallel computers -- Superblend coaxial mixer configuration -- Numerical model -- Hydrodynamics in Superblend coaxial mixer -- Mixing -- Mixing efficiency -- Parallel finite element solver -- Parallel sliding mesh technique -- Simulation of the hydrodynamics of a stirred tank in the transition regime -- Recommendations for future research -- Parallel algorithms -- Simulation of agited and the transition flow regime

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques