A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

Effect of hydrogen dilution on the deposition of carbon-rich a-SiC:H films by the electron cyclotron resonance method

The deposition of hydrogenated amorphous silicon carbide (a-SiC:H) films from a mixture of silane, acetylene and hydrogen gas using the electron cyclotron resonance chemical vapour deposition (ECR-CVD) process is reported. The variation in the deposition and film characteristics such as the deposition rate, optical band gap and IR absorption as a function of the hydrogen dilution is investigated. The deposition rate increases to a maximum value of about 250 Å min-1 at a hydrogen dilution ratio of about 20 (hydrogen flow (sccm)/acetylene + silane flow (sccm)) and decreases in response to a further increase in the hydrogen dilution. There is no strong dependence of the optical band gap on the hydrogen dilution within the dilution range investigated (10-60) and the optical band gap calculated from the E04 method varied marginally from about 2.85 to 3.17 eV. The room temperature photoluminescence (PL) peak energy and intensity showed a prominent shift to a maximum value of about 2.17 eV corresponding to maximum PL intensity at a moderate hydrogen dilution of about 30. The PL intensity showed a strong dependence on the hydrogen dilution variation.

Predicting shock response in uncertain structures using the Hybrid method

Using the Hybrid method (FE + SEA) it is possible to estimate the frequency response of an uncertain structure. The current work develops the Hybrid method to allow for time domain analysis of the shock response of a structure. Problems to be overcome when taking Hybrid method results into the time domain are a) the Hybrid method frequency response has no phase information, and b) the Hybrid method frequency response is smoothed in frequency and shows no modal peaks. In this paper the first problem has been overcome, using minimum phase reconstruction. Explanation of minimum phase reconstruction and its limitations are described, and application to shock problems described. © 2009 IOP Publishing Ltd.

Development and evaluation of an alternative method for processing elastic-lidar return signals

A method for interpreting elastic-lidar return signals in heavily-polluted atmospheres is presented. It is based on an equation derived directly from the classic lidar equation, which highlights gradients of the atmospheric backscattering properties along the laser optical path. The method is evaluated by comparing its results with those obtained with the differential absorption technique. The results were obtained from locating and ranging measurements in pollutant plumes and contaminated environments around central México. © World Scientific Publishing Company.

Subdivision-stabilised immersed b-spline finite elements for moving boundary flows

An immersed finite element method is presented to compute flows with complex moving boundaries on a fixed Cartesian grid. The viscous, incompressible fluid flow equations are discretized with b-spline basis functions. The two-scale relation for b-splines is used to implement an elegant and efficient technique to satisfy the LBB condition. On non-grid-aligned fluid domains and at moving boundaries, the boundary conditions are enforced with a consistent penalty method as originally proposed by Nitsche. In addition, a special extrapolation technique is employed to prevent the loss of numerical stability in presence of arbitrarily small cut-cells. The versatility and accuracy of the proposed approach is demonstrated by means of convergence studies and comparisons with previous experimental and computational investigations.