Robust multilevel methods for quadratic finite element anisotropic elliptic problems

This paper discusses a class of multilevel preconditioners based on approximate block factorization for conforming finite element methods employing quadratic trial and test functions. The main focus is on diffusion problems governed by a scalar elliptic partial differential equation with a strongly anisotropic coefficient tensor. The proposed method provides a high robustness with respect to non‐grid‐aligned anisotropy, which is achieved by the interaction of the following components: (i) an additive Schur complement approximation to construct the coarse‐grid operator; (ii) a global block (Jacobi or Gauss–Seidel) smoother complementing the coarse‐grid correction based on (i); and (iii) utilization of an augmented coarse grid, which enhances the efficiency of the interplay between (i) and (ii). The performed analysis indicates the high robustness of the resulting two‐level method. Moreover, numerical tests with a nonlinear algebraic multilevel iteration method demonstrate that the presented two‐level method can be applied successfully in the recursive construction of uniform multilevel preconditioners of optimal or nearly optimal order of computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

Structural transformation from shish‐kebab crystals to micro‐fibrils through hot stretching process of gel‐spun ultra‐high molecular weight polyethylene fibers with high concentration solution

Structural evolution of gel‐spun ultra‐high molecular weight polyethylene fibers with high concentration solution via hot stretching process was investigated by in situ small‐angle X‐ray scattering, in situ wide‐angle X‐ray diffraction measurements, scanning electron microscopy, and differential scanning calorimetry. With the increase of stretching strain, the long period continuously increases at relative lower stretching temperature, while it first increases and then decreases rapidly at relative higher stretching temperature. The kebab thickness almost keeps constant during the whole hot‐stretching process and the kebab diameter continually decreases for all stretching temperatures. Moreover, the length of shish decreases slightly and the shish quantity increases although there is almost no change in the diameter of shish crystals during the hot stretching process. The degree of crystal orientation at different temperatures is as high as above 0.9 during the whole stretching process. These results indicate that the shish‐kebab crystals in ultra‐high molecular weight polyethylene fibers can transform continuously into the micro‐fibril structure composed mostly of shish crystals through the hot stretching process. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 225–238     

Dithienylmethanone‐Based Cross‐Conjugated Polymer Semiconductors: Synthesis,Characterization, and Application in Field‐Effect Transistors

Herein, we report the synthesis, characterization, and field‐effect properties of two cross‐conjugated dithienylmethanone (DMO)‐based alternating polymers, namely, PDMO‐S and PDMO‐Se . Both polymers possess high thermal stability, good solubility, and broad absorption spectra. Their electrochemical properties were investigated using cyclic voltammetry, indicating that PDMO‐Se has higher HOMO/LUMO energy levels of −5.49/−3.49 eV than −5.57/−3.58 eV of PDMO‐S . The two polymers exhibited promising charge transport properties with the highest hole mobility of 0.12 cm² V⁻¹ s⁻¹ for PDMO‐S and 0.025 cm² V⁻¹ s⁻¹ for PDMO‐Se . AFM and 2D‐GIXRD analyses demonstrated that the PDMO‐S formed lamellar, edge‐on packing thin film with close π‐π stacking. These findings suggest that cross‐conjugated polymers might be potential semiconducting materials for low‐cost and flexible organic electronics. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 1012–1019     

The effect of methyl group on the mechanical properties of hydrophobic association hydrogel

Hydrophobic association hydrogels were fabricated via micellar copolymerization of acrylamide and hydrophobic monomers lauryl (meth)acrylate (LA or LMA) in an aqueous solution of sodium dodecyl sulfate. The effect of methyl groups of hydrophobic monomers on the crosslinking network structure and mechanical behavior of the gels was investigated on the basis of rubber elastic theory. It was found that the LMA-gel exhibited higher effective crosslink density and elastic modulus. The methyl groups of hydrophobic monomers limited the flexibility of the methacrylate backbone in the association domain, which resulted in the increment of chains constraints. With the increase of stretch rate, the dissipated energy of LMA-gel increased more highly than that of LA-gel. In addition, the methyl group hindered the movement of polymer chains, leading to the lower recovery efficiency of dissipated energy for LMA-gel. In contract, the LA-gel exhibited a rapid response to external force, and possessed better elasticity and self-recovery property. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1505–1512     

On the accuracy of a nonlinear finite volume method for the solution of diffusion problems using different interpolations strategies

In this paper, we consider a nonlinear finite volume method to solve the steady‐state diffusion equation in nonhomogeneous and non‐isotropic media. The method is nonlinear even if the original problem is linear. In its original form, the scheme is monotone, because the coefficient matrix is monotone under certain assumptions and, as a consequence, whenever the analytic operator demands, it preserves the positivity of numerical solutions. On the other hand, the scheme is unable to reproduce piecewise linear solutions exactly. In order to recover this interesting feature, we use two different interpolation strategies. In this case, even though we are unable to prove monotonicity, we show some numerical evidences that the combined method has an improved behavior, producing second order accurate solutions, even for nonhomogeneous and strongly anisotropic media. Copyright © 2013 John Wiley & Sons, Ltd.     

Brake Orbits of First Order Convex Hamiltonian Systems with Particular Anisotropic Growth

Combining the dual least action principle with Mountain-pass lemma,we obtain the existence of brake orbits for first-order convex Hamiltonian systems with particular anisotropic growth.