Efficient linear solvers for incompressible flow simulations using Scott‐Vogelius finite elements

Recent research has shown that in some practically relevant situations like multiphysics flows (Galvin et al., Comput Methods Appl Mech Eng, to appear) divergence‐free mixed finite elements may have a significantly smaller discretization error than standard nondivergence‐free mixed finite elements. To judge the overall performance of divergence‐free mixed finite elements, we investigate linear solvers for the saddle point linear systems arising in ((P_k)^d,P _k‐1^disc) Scott‐Vogelius finite element implementations of the incompressible Navier–Stokes equations. We investigate both direct and iterative solver methods. Due to discontinuous pressure elements in the case of Scott‐Vogelius (SV) elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements such as Taylor‐Hood elements. For direct methods, we extend recent preliminary work using sparse banded solvers on the penalty method formulation to finer meshes and discuss extensions. For iterative methods, we test augmented Lagrangian and \begin{align*}\mathcal{H}\end{align*} ‐LU preconditioners with GMRES, on both full and statically condensed systems. Several numerical experiments are provided that show these classes of solvers are well suited for use with SV elements and could deliver an interesting overall performance in several applications.© 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Minimally generated Boolean algebras

We introduce the class of minimally generated Boolean algebras, i.e. those algebras representable as the union of a continuous well-ordered chain of subalgebras A ₁ where A _i+1 is a minimal extension of A _i. Minimally generated algebras are closely related to interval algebras and superatomic algebras.     

Chemometric investigations on the differentiated evaluation of element trace analysis in river waters

The combination of sequential leaching methods for a first assessment of the kind of species in river sediments with multivariate-statistical methods (like factor analysis) for identifying anthropogenic and/or geogenic loading is useful for the differentiated characterization of the pollution state of a river. Electrochemical investigations, planned on the basis of statistical design and following empirical modelling, enables quantitative conclusions on the binding forms of heavy metals in river waters. Deposition-remobilisation effects of heavy metals in the complex system river water-river sediment can be described by PLS modelling.     

Quantitative SIMS depth profiling of diffusion barrier gate-oxynitride structures in TFT-LCDs

Gate oxynitride structures of TFT-LCDs were investigated by SIMS, and successful solutions are demonstrated to overcome difficulties arising due to the charging effects of the multilayer systems, the matrix effect of the method, and the small pattern sizes of the samples. Because of the excellent reproducibility achieved by applying exponential relative sensitivity functions for quantitative analysis, minor differences in the barrier gate-oxynitride composition deposited on molybdenum capped aluminium-neodymium metallisation electrodes were determined between the centre and the edge of the TFT-LCD substrates. No differences were found for molybdenum-tungsten metallisations. Furthermore, at the edge of the glass substrates, aluminium, neodymium, and molybdenum SIMS depth profiles show an exponential trend. With TEM micrographs an inhomogeneous thickness of the molybdenum capping is revealed as the source of this effect, which influences the electrical behaviour of the device.The production process was improved after these results and the aging behaviour of TFT-LCDs was investigated in order to explain the change in control voltage occurring during the lifetime of the displays. SIMS and TEM show an enrichment of neodymium at the interface to the molybdenum layer, confirming good diffusion protection of the molybdenum barrier during accelerated aging. The reason for the shift of the control voltage was finally located by semi-quantitative depth profiling of the sodium diffusion originating from the glass substrate. Molybdenum-tungsten was a much better buffer for the highly-mobile charge carriers than aluminium-neodymium. Best results were achieved with PVD silicon oxynitride as diffusion barrier and gate insulator deposited on aluminium-neodymium metallisation layers.