A new minimization protocol for solving nonlinear Poisson–Boltzmann mortar finite element equation

The nonlinear Poisson–Boltzmann equation (PBE) is a widely-used implicit solvent model in biomolecular simulations. This paper formulates a new PBE nonlinear algebraic system from a mortar finite element approximation, and proposes a new minimization protocol to solve it efficiently. In particular, the PBE mortar nonlinear algebraic system is proved to have a unique solution, and is equivalent to a unconstrained minimization problem. It is then solved as the unconstrained minimization problem by the subspace trust region Newton method. Numerical results show that the new minimization protocol is more efficient than the traditional merit least squares approach in solving the nonlinear system. At least 80 percent of the total CPU time was saved for a PBE model problem. AMS subject classification (2000)  65N30, 65H10, 65K10, 92-08     

The Mortar Element Method with Locally Nonconforming Elements

We consider a discretization of linear elliptic boundary value problems in 2-D by the new version of the mortar finite element method which uses locally nonconforming Crouzeix-Raviart elements. We show that if a solution of the original differential problem belongs to the space H ²(), then an error is of the same order as in the standard nonconforming finite element method. We also propose an additive Schwarz method of solving the discrete problem and show that its rate of convergence is almost optimal.     

A priori error analysis of the mortar finite element method for variational inequalities

The mortar finite element method is a special domain decomposition method, which can handle the situation where meshes on different subdomains need not align across the interface. In this article, we will apply the mortar element method to general variational inequalities of free boundary type, such as free seepage flow, which may show different behaviors in different regions. We prove that if the solution of the original variational inequality belongs to H²(D), then the mortar element solution can achieve the same order error estimate as the conforming P₁ finite element solution. Application of the mortar element method to a free surface seepage problem and an obstacle problem verifies not only its convergence property but also its great computational efficiency. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

水泥砂浆在主动围压下的动态力学性能

水泥砂浆等脆性材料的力学性能与所受围压的大小密切相关。为了研究水泥砂浆在围压下的动态力学性能,研制了适于分立式Hopkinson压杆加载的主动围压装置,最大预加载主动围压大于30 MPa。实验得到了水泥砂浆在不同围压、不同应变率下的轴向应力应变曲线,发现材料在围压作用下抗压强度和韧性大大提高并且整体进入了伪塑性,而材料的应变率效应也是显著的。     

基于细观力学方法的混凝土热膨胀系数预测

建立混凝土材料的有效性质与微结构参数之间的关系,是混凝土材料优化设计的基础。本文用细观力学方法对复合材料宏观有效热膨胀系数进行研究,得到了含有一球形夹杂物的无限大介质在均匀变温作用下的应力场。假定混凝土为由骨料和砂浆基质组成的二相复合材料,根据混凝土宏观体积热膨胀量与组成混凝土的各相介质细观体积热膨胀量相等的原则,采用基于Mori-Tanaka方法的混凝土宏观有效剪切模量,推导出混凝土有效热膨胀系数的解答。对稀疏解法、自洽方法和有限单元数值试验结果的比较说明,本文提出的基于自洽方法的混凝土宏观有效热膨胀系数的理论公式能够较好的描述混凝土的热学特性,该方法可以推广到多相复合材料宏观有效热膨胀系数的预测中。     

Mortar physical properties evolution in extrusion flow

Extrusion is not a common way to form firm cement-based material. Due to material frictional behaviour, drainage phenomenon appears and leads to process blockage. The properties of the extrusion multiphase flow of such specific materials have to be highlighted to understand the properties of the process flow. An extrudible mortar is formulated according to extrusion criteria provided by literature tests developed to describe the evolution of the paste undergoing extrusion. To study the relationship between flow properties, extrusion force and material consolidation, a technique based on the measurement of paste hardness in the billet zone is developed. Measurements of the local paste density and flow visualisation are also performed. Results show that in the range of used ram velocities, filtration occurs between fluid and solid phases. This creates zones of preferential flow and of non-flowing consolidated material. Paper presented at the 3rd Annual European Rheology Conference held on April 27–29, 2006, Crete, Greece.     

Physicochemical Characteristics of Styrene-Butadiene Latex- modified Mortar Composite vis-à-vis Preferential Interactions

The interaction between styrene-butadiene rubber (SBR) film and the ions from C₂S and C₃S hydration of Portland cement mortar composites has been evaluated by Fourier Transform Infrared Spectroscopy (FTIR), and the morphology of the composites characterized with scanning electron microscopy (SEM). The specimen used was cured for 28 days. FTIR spectrum supports the interaction of SBR with cement in the composite. Compressive strength, bulk density and water absorption properties of the cured composites were tested. Addition of SBR latex in Portland cement mortar increases the compressive strength and decreases the water absorption. Bulk density study revels interface formation in the composite. The role of the interface in relation to compressive strength of the composite has been discussed. A simple Matrix System model is shown to account composition dependence of bulk density.     

YDS高抗冲磨环氧砂浆的研究与应用

在YDS高渗透环氧化学灌浆材料的基础上,开发了一类新型高抗冲磨环氧砂浆。介绍了YDS高抗冲磨环氧砂浆的制备方法,探讨了环氧基液和环氧砂浆的主要性能。结果表明,YDS环氧砂浆不仅具有优异的抗渗耐腐蚀性能,而且其抗冲耐磨性能也非常好,抗冲磨强度最高达到400h/(kg/m2)以上,应用前景广泛。     

A regularized domain decomposition method with Lagrange multiplier

In this paper, we are concerned with the nonoverlapping domain decomposition method with Lagrange multiplier for three-dimensional second-order elliptic problems with no zeroth-order term. It is known that the methods result in a singular subproblem on each internal (floating) subdomain. To handle the singularity, we propose a regularization technique which transforms the corresponding singular problems into approximate positive definite problems. For the regularized method, one can build the interface equation of the multiplier directly. We first derive an optimal error estimate of the regularized approximation, and then develop a cheap preconditioned iterative method for solving the interface equation. For the new method, the cost of computation will not be increased comparing the case without any floating subdomain. The effectiveness of the new method will be confirmed by both theoretical analyzes and numerical experiments. The work is supported by Natural Science Foundation of China G10371129.     

A Dirichlet-Neumann Algorithm for Mortar Saddle Point Problems

A discretization of second order elliptic problems by the finite element method on nonmatching triangulation is discussed. The discrete problem is described as a saddle point problem obtained by a mortar technique. A Dirichlet-Neumann preconditioner is designed and analyzed for the discrete problem. It allows the use of an iterative preconditioner cg method with almost optimal rate of convergence.