A domain decomposition technique applied to the solution of the coupled electro‐mechanical problem

A domain decomposition approach for the solution of the coupled electro‐mechanical problem in dynamics is proposed. The finite element analysis of a coupled electro‐mechanical system is frequently found, for example, in the modelling and design of microsystems and may lead to a burdensome nonlinear problem solution, particularly in the dynamic case. Two versions of the algorithm are proposed: the first one, called single‐level decomposition, exploits the natural partition of the analysis domain given by the two physics to be solved; the second one, called two‐level decomposition, adds a further subdivision of each physics into subdomains. The multilevel domain decomposition strategy here proposed is shown to accurately predict the response of microsystems subjected to electro‐mechanical coupling and to allow for a significant reduction in the computational burden. Copyright © 2012 John Wiley & Sons, Ltd.     

A solution to Kronecker's problem

Consider [x ₁,...,x _n], the multivariate polynomial ring over integers involvingn variables. For a fixedn, we show that the ideal membership problem as well as the associated representation problem for [x ₁,...,x _n] are primitive recursive. The precise complexity bounds are easily expressible by functions in the Wainer hierarchy.Thus, we solve a fundamental algorithmic question in the theory of multivariate polynomials over the integers. As a direct consequence, we also obtain a solution to certain foundational problem intrinsic to Kronecker's programme for constructive mathematics and provide an effective version of Hilbert's basis theorem. Our original interest in this area was aroused by Edwards' historical account of theKronecker's problem in the context of Kronecker's version of constructive mathematics.Supported by an Italian grant Italian MURST 40% Calcolo Algebraico e Simbolico 1993 and an NSF grant: #CCR-9002819.     

A Frobenius solution to the scaled boundary finite element equations in frequency domain for bounded media

The scaled boundary finite element method (FEM) is a recently developed semi‐analytical numerical approach combining advantages of the FEM and the boundary element method. Although for elastostatics, the governing homogeneous differential equations in the radial co‐ordinate can be solved analytically without much effort, an analytical solution to the non‐homogeneous differential equations in frequency domain for elastodynamics has so far only been obtained by a rather tedious series‐expansion procedure. This paper develops a much simpler procedure to obtain such an analytical solution by increasing the number of power series in the solution until the required accuracy is achieved. The procedure is applied to an extensive study of the steady‐state frequency response of a square plate subjected to harmonic excitation. Comparison of the results with those obtained using ABAQUS shows that the new method is as accurate as a detailed finite element model in calculating steady‐state responses for a wide range of frequencies using only a fraction of the degrees of freedom required in the latter. Copyright © 2006 John Wiley & Sons, Ltd.     

A solution to the two-dimensional findpath problem

The 'findpath problem' a well-known problem in robotics, is the problem of finding a path for a moving solid among other solid obstacles. In this paper, a solution is proposed for the two-dimensional case where two point masses are required to move to designated areas or targets located in the horizontal plane while avoiding moving or stationary planar objects. The main tool used to solve the problem is the 'second or direct method of Liapunov', a powerful mathematical tool usually associated with the stability analysis of nonlinear systems. The theory developed from solving the two-dimensional findpath problem is then applied to the problem of cooperation between two planar robot arms. Computer simulations show the effectiveness of the proposed method     

A solution to the multiple set-up problem

This note finds the optimal order quantity for the multiple set-up problem. The solution is obtained by a direct method.     

A solution to the multivariable matrix factorization problem

Summary Given a para-Hermitian matrix,A(p ₁,p ₂, ...,p _n), whose elements are real, rational functions of the complex variablesp ₁,p ₂, ...,p _n, it is shown thatA (p ₁,p ₂, ...,p _n) can be factorized in the form,A (p ₁,p ₂, ...,p _n)=H ^t (–p ₁, –p ₂, ..., –p _n)H (p₁, p₂, ...,p _n), where the elements of the matrixH (p ₁,p ₂, ...,p _n) are also real rational functions of the specified variables, if and only ifA (j ₁, ...,j _n) is non-negative definite for all real _i, i=1, 2, ...,n. A rather simple computational method for the construction ofH (p ₁,p ₂, ...,p _n) is given, and examples are used to illustrate how, in many cases, the factorization can actually be carried to completion with little labour.     

Analysis of structures subjected to random wind loading by simulation in the frequency domain

The closely related methods of transfer matrices and direct numerical integration have been extensively used in the analysis of free standing structures. In case of structures subjected to dynamic loading, the method is particularly suitable to analysis in the frequency domain, enabling the consideration of arbitrary linear time-dependent material behaviour without additional difficulties. In this paper, a method is proposed to simulate stationary random processes in the frequency domain and it is applied for analysis of structures under along-wind action. The method requires less computational effort than standard procedures to obtain the power spectral density function of response quantities of interest and, since the solutions are obtained by simulation, may be extended to include in the formulation some types of non-linearity. Furthermore, it can be advantageously employed in the dynamic analysis of thin-walled open section beams, for which other alternatives are rarely available. The method proposed is applied to various free-standing towers and chimneys, for which response measurements are available, allowing a direct comparison of theoretical and experimental results.     

A boundary element solution to the soap bubble problem

The boundary element method (BEM) is applied to the soap bubble problem, that is to the problem of determining the surface that a soap bubble constrained by bounding contours assumes under the action of molecular forces. This is also the shape of a uniformly stretched membrane bounded by one or more non-intersecting curves. As the slopes of the membrane surface are finite, their square can not be neglected and the resulting governing equation is non-linear. The problem is solved using the analogue equation method (AEM). According to this method the non-linear membrane is substituted by a linear one subjected to a fictitious transverse load. The fictitious load is established using the BEM. Numerical examples are presented which illustrate the method and demonstrate its accuracy. This application of the BEM to non-linear problems shows that BEM is a versatile computational method for all-purpose use in engineering analysis. The solution of the problem at hand is very important in engineering, since the soap bubble surface can be used as the best initial form for membrane roofs.     

A simulated annealing solution to the cell formation problem

This research develops a simulated annealing (SA) based heuristic for cell formation problems. We apply the SA based heuristic to many popular examples for cell formation problems. The computational results show that the SA based heuristic performs very well in all these examples, and the SA based heuristic has several advantages that most of the existing algorithms do not have.     

A two-stage solution to the anisotropic polysilicon etching problem

A 2 micron MOS process can make many demands upon dry-etching techniques. The needs of one such process are outlined, together with the search for an etchant gas suitable for the production environment in question. The observed etching characteristics of two well-known contenders, Freon 115 and CCl₄ are described, leading to the development of a useful two-stage solution helped by the real time monitoring ability of a laser interferometric endpoint detector.The final process has been utilised for pilot production over a ten-month period, and is discussed in terms of performance and applications, being capable of batch-etching with less than 0.1 μm linewidth loss per feature, and less than 100 Å underlying SiO₂ loss.     

分支管流固耦合振动的频域解析解

利用拉氏变换,把时域流固耦合14方程模型变换到频域,对频域方程进行推导,得到12个一元四阶常微分方程和2个一元二阶常微分方程,对其求解,得到了直管的频域解析解。然后结合分支点的平衡条件以及分支管的边界条件,求解得出任意形状分支管的频域解析解。最后,对结果进行仿真计算,利用英国Dundee大学Tijsseling教授的实验结果对计算结果进行验证,并对不同形状的分支管进行了仿真计算。     

A frequency domain metamodeling approach to transient sensitivity analysis

This paper develops a metamodel approach to approximate the transient relationship between a univariate output response and one or more continuous-valued input factors in a computer simulation. The approach is based on a variant of Frequency Domain Methodology (FDM) in which a metamodel is hypothesized in the time domain; the analysis and parameter estimation are performed in the frequency domain; and finally prediction and inference are made back in the time domain. The switching of domains for analysis and estimation is advantageous because it permits the simultaneous consideration of multiple input factor changes. The metamodel is then used to estimate the mean transient function of the output response after a discontinuous change has been made to each individual input factor. The methodology is illustrated on an M/M/1 queue and a three-station tandem queue.     

Approximate matching-based unsupervised document indexing approach: application to biomedical domain

Scientometrics - Document indexing is considered as a crucial phase in the information retrieval field because textual information is constantly increasing. With this accumulation of documents, the...     

Iterative solution of a hybrid method for Maxwell's equations in the frequency domain

A hybrid method for solution of Maxwell's equations of electromagnetics in the frequency domain is developed as a combination between the method of moments and the approximation in physical optics. The equations are discretized by a Galerkin method and solved by an iterative block Gauss–Seidel method. The convergence of the iterations is studied theoretically and in numerical experiments. The accuracy of the hybrid method is compared to the method of moments for a cylinder with an incident field for different wavenumbers. Copyright © 2003 John Wiley & Sons, Ltd.     

A solution to the ‘training’ problem in superconducting magnets

A major factor in the design of large superconducting magnets is the problem of premature quenching, notably the ‘training’ effect, associated with the use of epoxy resin impregnants.This paper draws attention to the existence of a simple but neglected solution to this problem. A review is given of a series of tests carried out in 1968–1971 which showed that such effects were considerably reduced in the case of solenoid and quadrupole coils impregnated with wax or oil, allowing currents at least 85–90% of the critical value to be achieved consistently and reliably. The tests included a full scale prototype quadrupole (9 cm bore, 40 kG maximum field).A discussion of the mechanical and thermal properties of such coils indicates no reason to doubt their long term reliability, and the adoption of this solution for operational magnets is recommended.     

Transient heat conduction under nonzero initial conditions: A solution using the boundary element method in the frequency domain

A boundary element method formulation is proposed to solve the diffusion equation under nonzero initial conditions. The problem is solved in the frequency domain, considering only the conduction phenomenon. Complex frequencies are used to avoid aliasing and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of this approach for solving 2-D diffusion equations.