An adaptive multigrid technique for three-dimensional elasticity

A program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The solution process starts on an initial coarse mesh; here error estimators are determined by the standard Babu?ka-Rheinboldt method and local refinement is performed by partitioning of indicated elements, each hexahedron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following way-on the ith mesh only the elements caused by refinement on the (i-1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution method on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be successfully used for solving problems with structural singularities, such as re-entrant corners and moving boundary conditions. A numerical example shows that such problems are solved with the same efficiency as regular problems.     

Truly monolithic algebraic multigrid for fluid–structure interaction

The coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid–structure interaction by means of monolithic solution schemes. Therein, a Newton–Krylov method is applied to the monolithic set of nonlinear equations. Such schemes require good preconditioning to be efficient. We propose two preconditioners that apply algebraic multigrid techniques to the entire fluid–structure interaction system of equations. The first is based on a standard block Gauss–Seidel approach, where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem. The second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields. The resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance. Copyright © 2010 John Wiley & Sons, Ltd.     

An algebraic multigrid approach to solve extended finite element method based fracture problems

This article proposes an algebraic multigrid (AMG) approach to solve linear systems arising from applications where strong discontinuities are modeled by the extended finite element method. The application of AMG methods promises optimal scalability for solving large linear systems. However, the straightforward (or ‘black‐box’) use of existing AMG techniques for extended finite element method problems is often problematic. In this paper, we highlight the reasons for this behavior and propose a relatively simple adaptation that allows one to leverage existing AMG software mostly unchanged. Numerical tests demonstrate that optimal iterative convergence rates can be attained that are comparable with AMG convergence rates associated with linear systems for standard finite element approximations without discontinuities. Published 2012. This article is a US Government work and is in the public domain in the USA.     

An algebraic algorithm for nonuniformity correction in focal-plane arrays

A scene-based algorithm is developed to compensate for bias nonuniformity in focal-plane arrays. Nonuniformity can be extremely problematic, especially for mid- to far-infrared imaging systems. The technique is based on use of estimates of interframe subpixel shifts in an image sequence, in conjunction with a linear-interpolation model for the motion, to extract information on the bias nonuniformity algebraically. The performance of the proposed algorithm is analyzed by using real infrared and simulated data. One advantage of this technique is its simplicity; it requires relatively few frames to generate an effective correction matrix, thereby permitting the execution of frequent on-the-fly nonuniformity correction as drift occurs. Additionally, the performance is shown to exhibit considerable robustness with respect to lack of the common types of temporal and spatial irradiance diversity that are typically required by statistical scene-based nonuniformity correction techniques.     

求解矩形布局问题的自适应算法

矩形布局问题属于NP-Hard问题,其求解算法多为启发式算法。该文侧重于构造布局求解算法中定位函数(规则)的优化,将模拟退火算法的思想融入到遗传算法中,提出了求解矩形布局问题的自适应算法,其利用自适应交叉、变异及接收劣质解的概率等方法对定位函数中各参数进行优化。算法通过两种方式确定初始种群的数目,具有较强的适应性。在算法搜索的后期,利用差异性较大的个体进行交叉操作,从而保持种群的多样性。最后通过实例证明了该算法能够很好的应用于矩形布局问题的求解。     

An adaptive algorithm for nonlinear system identification

There are several methods — fixed, adaptive, recursive — for the identification of linear and bilinear systems from input-output measurements that are noisy. However, literature is rather scarce as far as such techniques are concerned for the identification of nonlinear systems. The objective of this paper, therefore, is to suggest an iterative technique for the identification of nonlinear system parameters from measurements that are noisy. This technique requires the transformation of a nonlinear system in the state variable form into an input-output autoregressive moving average exogenous (armax) model. The pseudo linear regression algorithm, which has been extensively used for the identification of linear systems, can then be used to identify the nonlinear system parameters. Using this technique simulation studies were carried out which, indeed, confirm the efficacy of the method.     

An algebraic algorithm for the resolution of singularities of foliations

We propose an algorithm that uses Gröbner bases to compute the resolution of the singularities of a foliation of the complex projective plane.     

一种改进的推广自适应相干累积算法

论文主要研究了LMS算法、ACI算法、GACI算法的原理和性能；并对GACI算法加以改进，以降低其参数对背景噪声变化的敏感性；将算法用来提取高斯白噪声背景下的线性调频脉冲信号，并用软件仿真器进行仿真。仿真结果表明了改进的GACI算法的优越性——参数对背景噪声功率变化的敏感性明显降低，并证明了其可靠性、可行性以及工程可实现性。     

硅微陀螺信号的自适应UKF滤波处理

针对硅微陀螺零偏重复性差和漂移信号中非线性因素的存在,提出利用AR模型系数实时递推方法对漂移信号进行AR建模,并建立相应的状态方程和量测方程;基于方差膨胀原则的自适应无迹Kalman滤波(AUKF)方法对漂移信号进行处理,采用简化的AUKF滤波过程提高漂移信号滤波的实时性。静态信号和动态测试处理结果表明,简化的AUKF算法效果明显优于UKF滤波和Kalman滤波(KF),滤波后硅微陀螺零偏稳定性提高倍数分别是UKF和KF的3倍和2倍,动态信号滤波后误差减少倍数分别是UKF和KF的1.46和1.34,信号均值不变,但AUKF需要较多的信号处理时间。     

Algorithms for refining triangular grids suitable for adaptive and multigrid techniques

Two general algorithms for refining triangular computational meshes based on the bisection of triangles by the longest side are presented and discussed. The algorithms can be applied globally or locally for selective refinement of any conforming triangulation and always generate a new conforming triangulation after a finite number of interactions even when locally used. The algorithms also ensure that all angles in subsequent refined triangulations are greater than or equal to half the smallest angle in the original triangulation; the shape regularity of all triangles is maintained and the transition between small and large triangles is smooth in a natural way. Proofs of the above properties are presented. The second algorithm is a simpler, improved version of the first which retains most of the properties of the latter. The algorithms can be used either for constructing irregular computational meshes or for locally refining any given triangulation. In this sense they can be adequately combined with adaptive and/or multigrid techniques for solving finite element systems. Examples of the application of the algorithms are given and two possible generalizations are pointed out.     

一种改进的自适应图像传感器数据插值算法

提出了一种改进的自适应插值算法,以改善传统图像传感器图像色调变化幅度过大,图像视觉效果不理想等问题.该算法适于硬件实现.数值实验证明,处理后图像的峰值信噪比有所提高.     

An algorithm for adaptive refinement of triangular element meshes

A simple algorithm is developed for adaptive and automatic h refinement of two-dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.     

An adaptive species conservation genetic algorithm for multimodal optimization

This paper introduces an adaptive species conservation genetic algorithm (ASCGA) by defining a species with three parameters: species seed, species radius and species boundary fitness. A species is defined as a group of individuals that have similar characteristics and that are dominated by the best individual in the species, called the species seed. Species radius defines the species' upper boundary and the species boundary fitness is the lowest value of fitness in the boundary. Some heuristic algorithms have been developed to adjust these parameters and an ASCGA has been proposed to solve multimodal optimization problems. With heuristic techniques, ASCGA can automatically adjust species parameters and allow the species to adapt to an optimization problem. Experimental results presented demonstrate that the proposed algorithm is capable of finding the global and local optima of test multimodal optimization problems with a higher efficiency than the methods from the literature. ASCGA has also successfully found a significantly different solution of a 25‐bar space truss design and identified 761 local solutions of the 2‐D Shubert function. Copyright © 2009 John Wiley & Sons, Ltd.     

An adaptive genetic algorithm for large-size open stack problems

The problem of minimising the maximum number of open stacks arises in many contexts (production planning, cutting environments, very-large-scale-integration circuit design, etc.) and consists of finding a sequence of tasks (products, cutting patterns, circuit gates, etc.) that determines an efficient utilisation of resources (stacks). We propose a genetic approach that combines classical genetic operators (selection, order crossover and pairwise interchange mutation) with an adaptive search strategy, where intensification and diversification phases are obtained by neighbourhood search and by a composite and dynamic fitness function that suitably modifies the search landscape. Computational tests on random and real-world benchmarks show that the proposed approach is competitive with the state of the art for large-size problems, providing better results for some classes of instances.     

An adaptive multi-population genetic algorithm for job-shop scheduling problem

Job-shop scheduling problem (JSP) is a typical NP-hard combinatorial optimization problem and has a broad background for engineering application. Nowadays, the effective approach for JSP is a hot topic in related research area of manufacturing system. However, some JSPs, even for moderate size instances, are very difficult to find an optimal solution within a reasonable time because of the process constraints and the complex large solution space. In this paper, an adaptive multi-population genetic algorithm (AMGA) has been proposed to solve this problem. Firstly, using multi-populations and adaptive crossover probability can enlarge search scope and improve search performance. Secondly, using adaptive mutation probability and elite replacing mechanism can accelerate convergence speed. The approach is tested for some classical benchmark JSPs taken from the literature and compared with some other approaches. The computational results show that the proposed AMGA can produce optimal or near-optimal values on almost all tested benchmark instances. Therefore, we can believe that AMGA can be considered as an effective method for solving JSP.     

Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of asphalt concrete, which is a mixture of components with large differences in material stiffness. The discontinuities in material stiffness give rise to many small eigenvalues that negatively affect the convergence of iterative solution algorithms such as the preconditioned conjugate gradient (PCG) method. This paper considers the deflated preconditioned conjugate gradient (DPCG) method in which the rigid body modes of sets of elements with homogeneous material properties are used as deflation vectors. As preconditioner we consider several variants of the algebraic multigrid smoothed aggregation method. We evaluate the performance of the DPCG method on a parallel computer using up to 64 processors. Our test problems are derived from real asphalt core samples, obtained using CT scans. We show that the DPCG method is an efficient and robust technique for solving these challenging linear systems.     

An improved multigrid method for Euler equations

A new full approximation storage multigrid method has been developed for Euler equations. Instead of the usual approach of using frozen τ (the relative truncation error between fine and coarse grid levels), the relative truncation error is distributed over coarse grids based on the solution of a set of model equations at every time step. This allows for more number of sweeps at coarse grid level. As a result, the present multigrid method is able to accelerate the solution at much faster rate than the conventional multigrid method. A first order Steger and Warming flux vector splitting strategy has been used here for solving Euler equations as well as the model equations for τ. Results are presented to demonstrate the ability of the present multigrid method.     

Nonlinear three-dimensional magnetic field computations usingLagrange finite-element functions and algebraic multigrid

The paper proposes an efficient solution strategy for nonlinear three-dimensional (3-D) magnetic field problems. The spatial discretization of Maxwell's equations uses Lagrange finite-element functions. The paper shows that this discretization is appropriate for the problem class. The nonlinear equation is linearized by the standard fixed-point scheme. The arising sequence of symmetric positive definite matrices is solved by a preconditioned conjugate gradient method, preconditioned by an algebraic multigrid technique. Because of the relatively high setup time of algebraic multigrid, the preconditioner is kept constant as long as possible in order to minimize the overall CPU time. A practical control mechanism keeps the condition number of the overall preconditioned system as small as possible and reduces the total computational costs in terms of CPU time. Numerical studies involving the TEAM 20 and the TEAM 27 problem demonstrate the efficiency of the proposed technique. For comparison, the standard incomplete Cholesky preconditioner is used     

MVDR自适应波束形成的一种智能算法

最小方差无失真响应（MVDR）自适应波束形成方法在声纳阵列信号处理中得到了广泛的应用。当存在强干扰时,传统的MVDR算法的稳定性较差,在有限次快拍数条件下,会带来一定的信噪比损失。将粒子群优化算法（PSO）引入MVDR的求解过程,提出了一种MVDR的数值实现方法。该方法在保持信号能量不变、干扰和噪声能量最小的约束条件下,利用粒子群优化算法通过数值搜索的方法获得MVDR的最优权向量。在小快拍数条件下,较一般的MVDR具有更好的抑制干扰能力。计算机仿真结果验证了该方法的有效性。     

An adaptive finite element algorithm for contact problems in plasticity

Due to the fact that in contact problems the contact area is not known a priori, a sufficient discretization to obtain a convergent finite element solution cannot be supplied from the outset. Therefore it is necessary to use adaptive finite element methods to adjust automatically the mesh sizes not only in the bodies under consideration but also in the contact zone. In this paper we develop an adaptive method for geometrically linear contact problems, which also includes elastoplastic material behavior. The radial return algorithm is used to derive the error estimator for one time increment of the solution process. The error estimator is based on the Zienkiewicz-Zhu projection scheme, which is extended to account for the special situation in the contact interface.In memoriam of J. C. Simo