Finite element simulations of fully non‐linear interaction between vertical cylinders and steep waves. Part 2: numerical results and validation

In Ma, Wu, Eatock Taylor [Finite element simulation of fully non‐linear interaction between vertical cylinders and steep waves. Part 1: methodology and numerical procedure. International Journal for Numerical Methods in Fluids 2001], designated Part 1 hereafter, we have developed the methodology and solution procedure for simulating the three‐dimensional interaction between fixed bodies and steep waves based on a finite element method (FEM). This paper provides extensive numerical results and validation. The effectiveness of the radiation condition is investigated by comparing the results from short and long tanks; the accuracy of the computed data is confirmed through comparison with analytical solutions. The adopted mathematical model is also validated by comparing the obtained numerical results with experimental data. Various test cases, including non‐linear bichromatic and irregular waves and the interactions between waves and one or two cylinders, are analysed. Copyright © 2001 John Wiley & Sons, Ltd.     

Adaptive finite element methods for the identification of distributed parameters in elliptic equation

In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments.      

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS(Ⅱ)—ALCULATION AND THE RESULTS

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Characterization of simple K 4-groups

In this paper, we prove that a group G is isomorphic to M, where M is a simple K ₄-group, if and only if the following hold: (1) |G| = |M|, (2) nse(G) = nse(M).      

A pseudo active kinematic constraint for a biological living soft tissue: An effect of the collagen network

Recent studies in mammalian hearts show that left ventricular wall thickening is an important mechanism for systolic ejection, and that during contraction the cardiac muscle develops significant stresses in the muscular cross-fiber direction. We suggested that the collagen network surrounding the muscular fibers could account for these mechanical behaviors. To test this hypothesis we develop a model for large deformation response of active, incompressible, nonlinear elastic and transversely isotropic living soft tissue (such as cardiac or arteries tissues) in which we include a coupling effect between the connective tissue and the muscular fibers. Then, a three-dimensional finite element formulation including this internal pseudo-active kinematic constraint is derived. Analytical and finite element solutions are in a very good agreement. The numerical results show this wall thickening effect with an order of magnitude compatible with the experimental observations.     

Progress and challenges in computational rheology

Our research work over the last few years serves to illustrate the basic issues associated with the numerical prediction of rheologically-complex flows, with particular emphasis on viscoelastic fluids. Numerical challenges in this field are shown to be tightly coupled to the mathematical nature of the governing equations, as well as to fundamental physical issues such as flow behavior close to walls and singularities.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

对象散全息元件产生的正交象散特性的研究

本文从理论上分析了用全息方法制作具有象散特征的一种光学元件——象散全息元件——的可能性,并得到实验上的证明.对由象散全息元件在空间正交方向上产生的象散特性作了较为仔细的研究,给出了实验结果.若用此元件代替普通象散系统,将具有使用方便,经济等优点.     

L-拓扑空间中的相对强F紧性与相对超F紧性

In this paper,two concepts of relative compactness-the relative strong fuzzy compactness and the relative ultra-fuzzy compactness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.     

抛物问题的mortar有限元逼近的瀑布型多重网格法

用瀑布型多重网格法解决椭圆、抛物问题，已有不少研究工作[1-2]，本文对抛物问题的mortar有限元的全离散格式提出瀑布型多重网格法，证明了该方法是最优的，即具有最优精确度和复杂度．     

On some nonlinear problems induced by an abstract maximal element principle

In this paper, by applying an abstract maximal element principle on quasi-ordered sets established by Lin and Du, we obtain a generalized Brézis–Browder principle, system (vectorial) versions of Ekeland's variational principle and maximal element principle and a vectorial version of Takahashi's nonconvex minimization theorem. Moreover, we investigate the equivalence between scalar versions and vectorial versions of these results.