On global Hessenberg based methods for solving Sylvester matrix equations

In the first part of this paper, we investigate the use of Hessenberg-based methods for solving the Sylvester matrix equation $AX+XB=C$. To achieve this goal, the Sylvester form of the global generalized Hessenberg process is presented. Using this process, different methods based on a Petrov–Galerkin or on a minimal norm condition are derived. In the second part, we focus on the SGl-CMRH method which is based on the Sylvester form of the Hessenberg process with pivoting strategy combined with a minimal norm condition. In order to accelerate the SGl-CMRH method, a preconditioned framework of this method is also considered. It includes both fixed and flexible variants of the SGl-CMRH method. Moreover, the connection between the flexible preconditioned SGl-CMRH method and the fixed one is studied and some upper bounds for the residual norm are obtained. In particular, application of the obtained theoretical results is investigated for the special case of solving linear systems of equations with several right-hand sides. Finally, some numerical experiments are given in order to evaluate the effectiveness of the proposed methods.     

Multiphase topology optimization with a single variable using the phase-field design method

In this study, a multimaterial topology optimization method using a single variable is proposed by combining the solid isotropic material with penalization method and the reaction-diffusion equation. Unlike ordinary multimaterial optimization, which requires several variables depending on the number of material types, this method intends to represent various materials as one variable. The proposed method combines two special functions in the sensitivity analysis of the objective function to converge the design variable into prespecified density values defined for each of the multimaterials. The composition constraint based on a normal distribution function is also introduced to estimate the distribution of each target density value in a single variable. It enables density exchange between multiple materials by increasing or decreasing the amount of a specific material. The proposed method is applied to structural and electromagnetic problems to verify its effectiveness, and its usefulness is also confirmed from the viewpoint of cost and computation time.     

A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients

In this paper, a combined compact finite difference method (CCD) together with alternating direction implicit (ADI) scheme is developed for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. The proposed CCD-ADI method is second-order accurate in time variable and sixth-order accurate in space variable. For the linear hyperbolic equation, the CCD-ADI method is shown to be unconditionally stable by using the Von Neumann stability analysis. Numerical results for both linear and nonlinear hyperbolic equations are presented to illustrate the high accuracy of the proposed method.     

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

On the numerical solution of Fredholm integral equations utilizing the local radial basis function method

The current investigation describes a computational technique to solve one- and two-dimensional Fredholm integral equations of the second kind. The method estimates the solution using the discrete collocation method by combining locally supported radial basis functions (RBFs) constructed on a small set of nodes instead of all points over the analysed domain. In this work, we employ the Gauss–Legendre integration rule on the influence domains of shape functions to approximate the local integrals appearing in the method. In comparison with the globally supported RBFs for solving integral equations, the proposed method is stable and uses much less computer memory. The scheme does not require any cell structures, so it is meshless. We also obtain the error analysis of the proposed method and demonstrate that the convergence rate of the approach is high. Illustrative examples clearly show the reliability and efficiency of the new method.     

一类Hilfer型分数阶微分方程解的存在和唯一性

用Banach不动点定理和上下解方法研究了α(1<α <2)阶数和β(0≤β ≤1)类型Hilfer分数阶微分方程的解,给出了方程解的存在和唯一性,并通过例证验证了本文所得结果的有效性.     

雷诺方程的数值计算方法概述

作为流体力学中的基本公式,雷诺方程的数值求解一直是流体润滑领域研究的重要方向之一。以雷诺方程的基本形式为基础,分别介绍有限差分法、有限元法和有限体积法求解雷诺方程的过程,讨论各自的特点及存在的问题;介绍多重网格法同上述方法结合在求解雷诺方程中的应用,指出多重网格法在求解雷诺方程的高效性方面有了很大程度的突破,但在求解精度上并未有显著改善;讨论等几何分析方法在求解雷诺方程上的应用,指出等几何分析方法求解雷诺方程具有较高的效率和求解精度,但仍存在如样条基函数的不可插值性和IGA在雷诺方程求解方面的普适性等问题,探讨IGA的研究方向,如针对特定雷诺方程引入适于IGA的新型样条表征求解空间、修改IGA理论与雷诺方程的离散模式引入新型边界条件加载模式等;因数值求解雷诺方程时在边界处理、复杂求解域等问题上仍没有一个稳定适用面广的方法,建议可尝试联合IGA与多重网格法来求解雷诺方程,以进一步提高求解效率和精度。     

离子液体的溶液热力学模型研究进展

离子液体是近年来发展起来的一种绿色介质，在化工反应和分离过程中具有广泛的应用前景。离子液体的溶液热力学性质和相平衡数据是其相关工艺过程设计的基础。本文从如下几个方面综述了离子液体溶液热力学模型的研究进展，即溶液热力学研究方法、溶液热力学模型的构建、离子液体的结构和分子间作用力、离子液体的溶液热力学模型及其在相平衡计算中的应用。重点分析了适用于离子液体溶液热力学性质计算的状态方程模型和过量Gibbs自由能模型或活度系数模型，离子液体的电解质和非电解质溶液模型，以及这些模型对ILs结构、氢键和静电作用的处理方法。分析了这些模型的优缺点，并对今后离子液体的溶液热力学研究提出了建议。     

Characterization of SiC ceramics with complex porosity by capillary infiltration: Part B – Filling by molten silicon at 1500 °C

In Part A of this study, infiltrations experiments of porous SiC samples by hexadecane with pore-size distributions comprising small and large pores were realized. Two successive stages were identified during the filling of these samples corresponding to the infiltration of the two types of pores. The experimental data were successfully treated with a new analytical function. In Part B, it was found that this function can also be applied to the analysis of the mass gain during molten silicon infiltration at 1500 °C. Prior to silicon infiltration, it was found that the operating temperature induces a shift of the pore size distributions towards larger values. A dissolution-recrystallisation mechanism can also occur during the infiltration of silicon. During the first stage, liquid silicon fills rapidly larger pores than hexadecane. The kinetics are significantly larger with liquid silicon. Consequently, the durations for the complete filling are very short with molten silicon.     

Emerging strategy recognition in agile portfolios

Agile practices become increasingly popular for projects and project portfolios offering firms a higher flexibility to adapt to dynamic environments. This study investigates the antecedents and consequences of agile practices' relevance for strategy formulation in project portfolio management processes. Building on complex adaptive systems theory, we hypothesize a positive relationship between agile capabilities and emerging strategy initiatives and eventually portfolio success. Agile capabilities refer to both the project portfolio organization's intensity of and competence in applying agile practices. Using a sample of 135 portfolios and multiple informants for each portfolio, the results support entrepreneurial orientation and voice behavior as antecedents for agile capabilities. Furthermore, the findings support an agile portfolio's positive relationship with emergence recognition and overall portfolio success. The findings contribute to the literature by identifying two significant antecedents of agile capabilities as well as empirically demonstrating the positive relationship between agile portfolios and emerging strategy recognition. For practitioners, the study encourages the application of agile practices by stressing the general positive influence of agile capabilities and underlines entrepreneurial orientation and voice behavior as important methods of empowerment for agile portfolio processes.