A methodology for quadrilateral finite element mesh coarsening

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedral meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. In addition, this method appears to be extensible to hexahedral meshes in three dimensions. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.     

A Numerical Study of Diagonally Split Runge–Kutta Methods for PDEs with Discontinuities

Diagonally split Runge–Kutta (DSRK) time discretization methods are a class of implicit time-stepping schemes which offer both high-order convergence and a form of nonlinear stability known as unconditional contractivity. This combination is not possible within the classes of Runge–Kutta or linear multistep methods and therefore appears promising for the strong stability preserving (SSP) time-stepping community which is generally concerned with computing oscillation-free numerical solutions of PDEs. Using a variety of numerical test problems, we show that although second- and third-order unconditionally contractive DSRK methods do preserve the strong stability property for all time step-sizes, they suffer from order reduction at large step-sizes. Indeed, for time-steps larger than those typically chosen for explicit methods, these DSRK methods behave like first-order implicit methods. This is unfortunate, because it is precisely to allow a large time-step that we choose to use implicit methods. These results suggest that unconditionally contractive DSRK methods are limited in usefulness as they are unable to compete with either the first-order backward Euler method for large step-sizes or with Crank–Nicolson or high-order explicit SSP Runge–Kutta methods for smaller step-sizes. We also present stage order conditions for DSRK methods and show that the observed order reduction is associated with the necessarily low stage order of the unconditionally contractive DSRK methods. The work of C.B. Macdonald was partially supported by an NSERC Canada PGS-D scholarship, a grant from NSERC Canada, and a scholarship from the Pacific Institute for the Mathematical Sciences (PIMS). The work of S. Gottlieb was supported by AFOSR grant number FA9550-06-1-0255. The work of S.J. Ruuth was partially supported by a grant from NSERC Canada.     

Level Set Equations on Surfaces via the Closest Point Method

Level set methods have been used in a great number of applications in ?² and ?³ and it is natural to consider extending some of these methods to problems defined on surfaces embedded in ?³ or higher dimensions. In this paper we consider the treatment of level set equations on surfaces via a recent technique for solving partial differential equations (PDEs) on surfaces, the Closest Point Method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943–1961, [2008]). Our main modification is to introduce a Weighted Essentially Non-Oscillatory (WENO) interpolation step into the Closest Point Method. This, in combination with standard WENO for Hamilton–Jacobi equations, gives high-order results (up to fifth-order) on a variety of smooth test problems including passive transport, normal flow and redistancing. The algorithms we propose are straightforward modifications of standard codes, are carried out in the embedding space in a well-defined band around the surface and retain the robustness of the level set method with respect to the self-intersection of interfaces. Numerous examples are provided to illustrate the flexibility of the method with respect to geometry.     

A referential scheme for modeling and identifying spatial attributes of entities in constructed facilities

This paper presents a referential scheme for representing and identifying the spatial extent of physical entities of constructed facilities, such as buildings and offshore structures. Using the basic operations of a non-manifold geometric modeler, a set of high-level algebraic operations is defined. The scheme and its algebra are used for modeling the spatial attributes of a facility entity at two levels: primary and secondary. The primary representation uniquely captures an entity's spatial attributes at the skeletal level and is used mainly for identifying discipline-independent topological relationships of that entity with others. Secondary representations, on the other hand, are used to provide an entity's discipline-specific geometric attributes. The topological relationships and geometric attributes of facility entities thus need not be explicitly stored, but can be computed on demand by the underlying non-manifold modeler.     

Analysis of dithiocarbamate fungicides. Second-derivative UV-spectroscopic determination of CS2, COS, and thiram (TMTD)

The application of second-derivative UV-spectroscopy offers a highly sensitive and selective method for the determination of CS₂ and COS, as acid hydrolysis products of dithiocarbamate und thiuram disulphide fungicides, using a methanolic amine absorption reagent (ethylenediamine, piperidine). With standard concentrations of 0.08–1.1 g CS₂/ml and 0.3 to 2.0 g COS/ml, respectively, calibration curves with good correlation coefficients (r>0.999) were obtained. In comparison to the official method of the Deutsche Forschungsgemeinschaft (DFG method S15) the proposed alternative is at least 100 times more sensitive to CS₂. Using the second derivative method it is possible not only to clearly differentiate between CS₂ and COS but also to quantify both gases without resorting to tedious background corrections as compared to the direct photometric methods. Additionally, second derivative spectroscopy allows the direct determination of thiram in the concentration range 1–10 g/ml after its extraction with chloroform. For example, thiram in water (10 g/l) and in thiram/talc standards (10 mg/g) were determined with good precision (±2.0%).

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Analytik der Dithiocarbamat-Fungicide. Bestimmung von CS₂, COS sowie Thiram (TMTD) mittels Derivativ-UV-Spektroskopie

Zusammenfassung Die Anwendung der Derivativ-UV-Spektroskopie (2. Ableitung) erlaubt eine sehr empfindliche Bestimmung von CS₂ und COS als Hydrolyseprodukte der Dithiocarbamat- und Thiuramdisulfid-Fungicide nach Absorption in einem methanolischem Amin-Reagens (Ethylendiamin, Piperidin). Mit Standard-Konzentrationen von 0,08–1,1 g CS₂/ml bzw. 0,3–2,0 g COS/ml zeigten die Eichgeraden gute Korrelationskoeffizienten (r<0,999). Im Vergleich zur DFG-Methode S15 zeichnet sich die vorgeschlagene Alternative durch eine um zwei Zehnerpotenzen höhere Empfindlichkeit bei der CS₂-Bestimmung aus. In der 2. Ableitung wird nicht nur die Unterscheidung von COS und CS₂ eindeutig, sondern auch deren Quantifizierung ohne rechnerische Untergrundkorrekturen ermöglicht. Mit Hilfe der Derivativspektroskopie konnte außerdem Thiram (TMTD) in Konzentrationen von 1–10 g/ml direkt erfaßt werden. So ließen sich nach Extraktion mit Chloroform 10 g/L Thiram in Wasser mit einer Präzision von ±2,0% direkt bestimmen oder Thiram/Talkum-Standards (10 mg/g) überprüfen.

     

One weight $$\mathbb {Z}_2\mathbb {Z}_4$$ additive codes

We study one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes. It is shown that the image of an equidistant \(\mathbb {Z}_2\mathbb {Z}_4\) code is a binary equidistant code and that the image of a one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive code, with nontrivial binary part, is a linear binary one weight code. The structure and possible weights for all one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes are described. Additionally, a lower bound for the minimum distance of dual codes of one weight additive codes is obtained.     

Isolation and identification of (3-methoxyphenyl)acetonitrile as a phytotoxin from meadowfoam (Limnanthes alba) seedmeal

Ethyl ether, ethanol, and water extracts of meadowfoam (Limnanthes alba Hartweg ex. Benth.) seedmeal were prepared and bioassayed against velvetleaf (Abutilon theophrasti Medicus) and wheat (Triticum aestivum L. Cardinal). Both the ethyl ether and ethanol fractions, but not the water extract, inhibited velvetleaf and wheat radicle elongation. Fractionation of the extracts indicated that (3-methoxyphenyl)acetonitrile (3-MPAN) was the active compound from both extracts, comprising >97% of the active ethanol fraction. 3-Methoxybenzyl isothiocyanate, which had been previously shown to be the major breakdown product of glucolimnanthin, the majorL. alba glucosinolate, was not detected in either extract. Radicle elongation of velvetleaf and wheat were inhibited by 3-MPAN with I₅₀ (the concentration required to inhibit growth by 50%) values of approximately 4 × 10^–4 M (velvetleaf) and 7×10^–4 M (wheat).Mention of firms or products does not imply endorsement by the U.S. Department of Agriculture over other firms or products not mentioned.