Adaptive remeshing for ductile fracture prediction in metal formingRemaillage adaptatif pour la prévision de la rupture ductile en mise en forme

The analysis of mechanical structures using the Finite Element Method in the framework of large elastoplastic strain, needs frequent remeshing of the deformed domain during computation. Indeed, the remeshing is due to the large geometrical distortion of finite elements and the adaptation to the physical behavior of the solution. This paper gives the necessary steps to remesh a mechanical structure during large elastoplastic deformations with damage. An important part of this process is constituted by geometrical and physical error estimates. The proposed method is integrated in a computational environment using the ABAQUS/Explicit solver and the BL2D-V2 adaptive mesher. To cite this article: H. Borouchaki et al., C. R. Mecanique 330 (2002) 709–716.     

Montgomery Multiplication in GF(2k)

We show that the multiplication operation c=a · b · r^-1 in the field GF(2^k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF(2^k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.     

Computation of the quasi-stationary distributions inM(n)/GI/1/K andGI/M(n)/1/K queues

In this paper, we provide numerical means to compute the quasi-stationary (QS) distributions inM/GI/1/K queues with state-dependent arrivals andGI/M/1/K queues with state-dependent services. These queues are described as finite quasi-birth-death processes by approximating the general distributions in terms of phase-type distributions. Then, we reduce the problem of obtaining the QS distribution to determining the Perron-Frobenius eigenvalue of some Hessenberg matrix. Based on these arguments, we develop a numerical algorithm to compute the QS distributions. The doubly-limiting conditional distribution is also obtained by following this approach. Since the results obtained are free of phase-type representations, they are applicable for general distributions. Finally, numerical examples are given to demonstrate the power of our method.     

Rank, term rank, and chromatic number

Let G be a graph with a nonempty edge set, and with rank rk(G), term rank Rk(G), and chromatic number χ(G). We characterize Rk(G) as being the maximum number of colors in certain proper colorings of G. In particular, we observe that χ(G)Rk(G), with equality holding if and only if (besides isolated vertices) G is either complete or a star. For a twin-free graph G, we observe the bound and we show that this bound is sharp.     

Optimal algebraic multilevel preconditioning for local refinement along a line

The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.     

三系数有限元向量尺度函数的构造

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.     

浅水中污染物扩散的自适应有限元分析法

介绍浅水中污染物扩散分析中的有限元法.分析包括两个部分:1)流场速度、水面高度的计算;2)根据扩散模型计算污染物浓度场.联合使用了自适应网格技术以期提高解的精度,同时减少计算时间和计算机内存的消耗.通过几个有已知解的实例验证了有限元公式和计算机程序.最后,使用这种联合方法分析泰国Chao Phraya河附近海湾中的污染物扩散.     

Finite element modal solutions of planar photonic crystal fibers with rectangular air-holes

Modal solutions of planar photonic crystal waveguides with rectangular air-holes are presented by using a rigorous full-vectorial finite element-based approach. The effective indices, mode field profiles, spot-sizes, power confinements, modal hybridness, beat lengths and group velocity dispersions are shown for the fundamental and higher order modes of the quasi-TE and TM polarizations.     

Fast algorithms for determining the linear complexities of sequences over GF(pm) with the period 3n

In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF(p ^m) (any positive integer m) with the period 3n (n and p ^m − 1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura algorithm, we can determine the linear complexity of any sequence over GF(p ^m) with the period 3n (n and p ^m − 1 are coprime) more efficiently.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002