Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Π_m leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Π_m for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Π_m+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered.     

The analysis of a finite element method for the three-species Lotka–Volterra competition-diffusion with Dirichlet boundary conditions

A Galerkin finite element method is developed for the two dimensional/three dimensional nonlinear time-dependent three-species Lotka–Volterra competition-diffusion equations on a bounded domain. The existence and uniqueness of the solution to the numerical formulation are proved. An error estimate for the numerical solution is obtained. Numerical computations are carried out to examine the expected orders of accuracy in the error estimates.     

Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson's ratio(PR)are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials' auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.     

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

Blended silicone-ionic liquid membranes: Transport properties of butan-1-ol vapor

This paper is focused on modeling of sorption and desorption kinetics as well as on equilibrium butan-1-ol vapor sorption in blended poly(dimethylsiloxane)-benzyl-3-butylimidazolium tetrafluoroborate membranes. Based on the generalized Fick’s second law, on time-dependent boundary conditions and on two models of equilibrium sorption, the diffusion coefficients of butan-1-ol were calculated from the experimental data using the finite difference modeling. Although anomalous sorption occurred at higher concentrations of butan-1-ol, the diffusion coefficients calculated from the data on sorption and desorption kinetics were in a good agreement. The increase of the ionic liquid content in poly(dimethylsiloxane) elevated the butan-1-ol equilibrium concentration in the membrane, and, at the same time, decreased the values of butan-1-ol diffusion coefficient.     

Variational reactive scattering calculations: computational optimization strategies

Summary We have developed efficient and accurate techniques for the calculation of quantum mechanical reaction probabilities of atom-diatom exchange reactions in the gas phase, and we have optimized a computer code employing these techniques and applied it sucessfully to several systems. In this paper we consider further strategies for improving the algorithm to allow even more demanding applications. In this context, improvement means that equivalent results can be obtained using fewer computational resources (computer time or storage) or that an equivalent expenditure of resources can yield higher accuracy. The new strategies discussed here lead to improvement in both of these areas. Two areas of special focus in the present paper are (i) the finite difference boundary value method used for calculating distorted wave Green's functions and regular solutions for scattering by the distortion potential and (ii) the choice of the distortion potential itself. Among other results included here is the first application of the outgoing wave or scattered wave variational principle to reactive scattering.     

Large orbit sizes in finite group actions

In this paper, we study the relations of the sizes of various sections of finite linear groups and the largest orbit size of the linear group actions. We also study various applications of those orbit theorems.     

A note on isodual constacyclic codes

This note gives a counterexample of Theorem 20 in the paper of Blackford (2013) [2]. The counterexample shows that [2, Theorem 20] is incorrect. Furthermore, we provide corrections to the above result.     

A new model for the analysis of reinforced concrete members with a coupled HdBNM/FEM

As a truly boundary-type meshless method, the hybrid boundary node method (HdBNM) does not require ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. In this paper, the HdBNM is coupled with the finite element method (FEM) for predicting the mechanical behaviors of reinforced concrete. The steel bars are considered as body forces in the concrete. A bond model is presented to simulate the bond-slip between the concrete and steels using fictitious spring elements. The computational scale and cost for meshing can be further reduced. Numerical examples, in 2D and 3D cases, demonstrate the efficiency of the proposed approach.