Unconditionally convergent partitioned solution procedure for dynamic coupled mechanical systems

A new partitioned solution procedure for the direct time integration of second order coupled-field systems is presented and it is applied to the problem of soil–pore fluid interaction. The necessary convergence analysis for the iterative method is carried out and the fulfilment of the convergence condition is achieved with the introduction of two suitable auxiliary matrices in the basic equations governing the dynamic phenomena. Numerical examples are presented to demonstrate the effectiveness and the versatility of the proposed solution procedure.     

Parallel eigenanalysis of multiaquifer systems

Finite element discretizations of flow problems involving multiaquifer systems deliver large, sparse, unstructured matrices, whose partial eigenanalysis is important for both solving the flow problem and analysing its main characteristics. We studied and implemented an effective preconditioning of the Jacobi–Davidson algorithm by FSAI‐type preconditioners. We developed efficient parallelization strategies in order to solve very large problems, which could not fit into the storage available to a single processor. We report our results about the solution of multiaquifer flow problems on an SP4 machine and a Linux Cluster. We analyse the sequential and parallel efficiency of our algorithm, also compared with standard packages. Questions regarding the parallel solution of finite element eigenproblems are addressed and discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

A posteriori analysis and adaptive error control for operator decomposition solution of coupled semilinear elliptic systems

In this paper, we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems. The goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation (discretization) and operator decomposition iteration. In an earlier paper, we considered ‘triangular’ systems that can be solved without iteration. In contrast, operator decomposition iterative methods for fully coupled systems involve an iterative solution technique. We construct an error estimate for the numerical approximation error that specifically addresses the propagation of error between iterates and provide a computable estimate for the iteration error arising because of the decomposition of the operator. Finally, we develop an adaptive discretization strategy to systematically reduce the discretization error.Copyright © 2013 John Wiley & Sons, Ltd.     

Comparison of laser ablation and dried solution aerosol as sampling systems in inductively coupled plasma mass spectrometry

This paper describes a study designed to determine the possibility of using a dried aerosol solution for calibration in laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The relative sensitivities of tested materials mobilized by laser ablation and by aqueous nebulization were established, and the experimentally determined relative sensitivity factors (RSFs) were used in conjunction with aqueous calibration for the analysis of solid steel samples. To such a purpose a set of CRM carbon steel samples (SS-451/1 to SS-460/1) were sampled into an ICP-MS instrument by solution nebulization using a microconcentric nebulizer with membrane desolvating (D-MCN) and by laser ablation (LA). Both systems were applied with the same ICP-MS operating parameters and the analyte signals were compared. The RSF (desolvated aerosol response/ablated solid response) values were close to 1 for the analytes Cr, Ni, Co, V, and W, about 1.3 for Mo, and 1.7 for As, P, and Mn. Complementary tests were carried out using CRM SS-455/1 as a solid standard for one-point calibration, applying LAMTRACE software for data reduction and quantification. The analytical results are in good agreement with the certified values in all cases, showing that the applicability of dried aerosol solutions is a good alternative calibration system for laser ablation sampling.     

A tightly coupled numerical foil bearing solution

Equations describing the steady-state flying height of magnetic tape over a recording head are solved using an algorithm that incorporates a linearized approximation of air bearing stiffness into the tape equation. The one-dimensional infinitely wide equations include compressibility and slip flow in the air bearing, as well as tension, momentum, and flexural rigidity in the tape. The stiffness coupling between the equations allows simulation of complicated head geometries and reduces the computational effort required to determine the steady-state flying height by more than an order of magnitude compared to previously published methods which are based on time-dependent equations. Two example problems are presented, both of which were solved on a personal computer in under one minute     

Parallel systems under two sequential attacks

The paper compares the efficiency of single and double attack against a system consisting of identical parallel elements (1-out-of-N system). An attacker tries to maximize the system vulnerability (probability of total destruction). The attacker distributes its constrained resource optimally across two attacks and chooses the number of elements to be attacked in the first attack. The attacker observes which elements are destroyed and not destroyed in the first attack, and applies its remaining resource into attacking the remaining elements in the second attack. First the optimal attack strategy against a system with a fixed number of elements is analyzed. Thereafter a minmax two period game between the attacker and the defender is considered in which the defender distributes its constrained resource between deploying redundant elements and protecting them against the attack.     

Parallel programming of a peridynamics code coupled with finite element method

Using OpenMP (the Open Multi- Processing application programming interface), dynamic peridynamics code coupled with a finite element method is parallelized. The parallel implementation improves run-time efficiency and makes the realistic simulation of crack coalescence possible. To assess the accuracy and efficiency of the parallel code, we investigate its speedup and scalability. In addition, to validate the parallel code, experimental results for crack coalescence development sequences are compared. It is noted that this parallelized code markedly reduces computation time along with the coupling scheme. Moreover, the coupling approach used in this parallel code enables a more realistic and feasible numerical prediction of coalescing fractures. With the parallel implementation, two main types of crack coalescences between two flaws, formed by two short shear cracks and by a short central tensile segment and subsequent shear cracks are in detail discussed in terms of their development sequences. Consequently, this proposed coupled peridynamics code can be used to efficiently solve actual coalescence development sequences, thereby providing a numerical solution for fracture mechanics.     

Parallel processing in dynamic simulation of power systems

The dynamic behaviour of a large interconnected electric power system is characterized by a simultaneous set of nonlinear algebraic and ordinary differential equations. The solution is obtained by numerical methods and the simulation of the transient behaviour for a few seconds after a fault is the standard analytical procedure used in planning and operational studies of the system. The need for on-line simulation in near real time for more efficient operation has encouraged the search for faster solution methods and the use of parallel computers for this purpose has attracted the attention of many researchers. The success of parallelization depends on three factors: the problem structure, the computer architecture, and the algorithm that takes maximum advantage of both. In this problem, the generator equations are only coupled through the electrical network providing some parallelization in (variable) space, and a solution is needed at each time step leading to some parallelization in time (waveform relaxation). However, since the problem formulation is not completely decoupled, parallel algorithms can only be developed by trading off any relaxation with a degradation in convergence. The fastest sequential algorithm used today is the combination of implicit trapezoidal integration with a dishonest Newton solution. The Newton algorithm is not parallel at all but has the fastest convergence while a Gauss-Jacobi algorithm is completely parallel but converges very slowly. A relaxation of the Newton algorithm appears to be a good compromise. As for the parallel hardware, the coupling seems to require significant communication between processors thus favouring a data-sharing architecture over a message-passing hypercube. Special architectures to match the problem structure have also been an area of investigation. This paper elaborates on the above issues and assesses the present state-of-the-art.     

Eigenproblem solution of damped structural systems

This article presents an efficient numerical algorithm a complete listing of the associated computer program, developed for the eigenproblem solution of discrete damped structures, including spinning ones. The numerically stable procedure is based on a combined Sturm sequence and inverse iteration technique, which fully exploits the banded form of the relevant matrices and proves to be most substantially economical when compared to similar existing softwares. Numerical results are presented for representative structures, solved by the present computer program written in FORTRAN V for the JPL UNIVAC 1108 computer.     

结构-声场耦合系统声压响应优化设计研究

为了减小结构振动产生的噪声,基于结构-声场耦合有限元模型,对其在简谐力激励下的声响应进行了计算。在此基础上,以结构厚度为设计变量,保持结构重量相对不变并以设计变量的上、下限为约束,以设计域点在各频率响应声压平方和的平方根为目标函数,对其进行了优化设计研究。用软件N astran计算声响应及声敏度,基于iS IGHT对N astran的集成用可行方向法实施了优化。以一矩形板结构-立方体声场耦合系统为实例,得到了优化的结构厚度分布。优化后,设计域点的峰值声压级均有不同程度的降低,声压级降低最大值达32.8dB。结果表明声压响应优化设计,在保持结构重量相对不变的情况下,通过对结构重量的重新分布能达到较明显的降噪效果。     

松耦合感应电能传输系统的设计

在建立感应电能传输系统互感模型的基础上，结合设计的小功率感应电源试验平台，分析了如何选择该系统的补偿拓扑年口谐振频率，根据分析结果搭建了感应电源试验平台，并且通过实验，证明了该系统在额定负载下的输出功率最大．     

Non-iterative solution of a tridiagonal-type matrix coupled by diagonal submatrices

A non-iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back-substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is included.     

Invariant form of the general solution of coupled dynamic thermoelastic problems

Field equations of coupled dynamic thermoelasticity are subjected to integral transformations in a finite domain. Repeated application of the generalized Green's theorem enables to find both the displacement and the temperature distribution in form of infinite series depending on boundary and initial conditions. Derived expressions are applied, as an example, to a parallelepiped with special boundary conditions.     

Synchronization of coupled bistable chaotic systems: experimental study

We carried out an experimental study of the synchronization of two unidirectionally coupled R?ssler-like electronic circuits with two coexisting chaotic attractors. Different stages of synchronization are identified on the route from asynchronous motion to complete synchronization, as the coupling parameter is increased: intermittent asynchronous jumps between coexisting attractors; intermittent anticipating phase synchronization; and generalized synchronization in the form of subharmonic entrainment terminated by complete synchronization. All these regimes are analysed with time-series, power spectra and phase-space plots of the drive and response oscillators. The experimental study implicitly confirms the results of numerical simulations.     

Mutual synchronization of switching processes in coupled Lorenz systems

A numerical analysis is made of the synchronization of the mean switching frequencies in two symmetrically coupled Lorenz systems functioning in a chaotic regime. The observed effect on the coupling-mismatch parameter plane corresponds to a region of synchronization of the switching processes, within which the mean switching frequencies coincide to a given accuracy. Pis’ma Zh. Tekh. Fiz. 23, 14–19 (April 26, 1997)     

Appearance of generalized synchronization in mutually coupled beam-plasma systems

The phenomenon of generalized synchronization onset between mutually coupled beam-plasma systems (Pierce diodes) with supercritical currents has been discovered. It is established that the appearance of a synchronous regime is related to the change in one Lyapunov exponent from a positive to negative value. The results of the analysis are confirmed by the nearest-neighbor method.     

Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators

We consider the dynamics of networks of oscillators that are weakly dissipative perturbations of identical Hamiltonian oscillators with weak coupling. Suppose the Hamiltonian oscillators have angular frequency y ( f ) when their energy is f . We address the problem of what happens in a neighbourhood of where d y /d f = 0; we refer to this as a point of isochronicity for the oscillators. If the coupling is much weaker than the dissipation we can use averaging to reduce the system to phase equations on a torus. We consider example applications to two and three weakly diffusively coupled oscillators with points of isochronicity and reduce to approximating flows on tori. We use this to identify bifurcation of various periodic solutions on perturbing away from a point of isochronicity.