Search results

The spectral boundary element method for solving two‐dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady‐state example of a semi‐infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time‐varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

An introduction is given to the generation and use of new transform techniques which have important applications in binary control and processing methods. A comparison is made between the fast Fourier transform and the equivalent fast Walsh transform together with the steps required to produce a transform algorithm and computer program. Some applications of the transform are then discussed and which include spectral analysis, filtering, non‐linear control and communications uses. 18 references to current work in these applications areas are included.

Combines the techniques of fast Fourier transforms, Buneman cyclic reduction and the capacity matrix in a finite difference Poisson solver specifically designed for modelling realistic electronic device structures. A solution may be determined on a number of connected rectangular regions which correctly accounts for continuity of the electric displacement at dielectric interfaces. Suggests the method is particularly well suited to problems requiring repeated solution with the same device structure and provides a self‐consistent Monte Carlo simulation as an example of such an application.

In this paper, two transform methods, the Fourier transform (FT) and the wavelet transform (WT) methods, are utilized to process moiré fringes for the strain analysis of electronic packaging. With the introduction of fringe carriers, those transform techniques need only one fringe pattern for each deformation state. The strain modulation to the carrier frequency can be subtracted by filtering as the pattern is transformed into spectrum domain by the fast‐FT processing, and the deformation field can thus be restored by the inverse FT transform after spectral shifting. The WT method expands the pattern information involved in the fringe carrier in both spatial domain and spectral domain to analyze the deformation distribution in this combined space. By changing the transform scales in the processing, the wavelet transform offers multi‐resolution analysis for the deformation field with high gradients.

This paper presents a methodology, based on the fast Fourier transform (FFT), that improves prior established techniques to solve axisymmetric potential problems with non‐axisymmetric boundary conditions using the boundary element method (BEM). The proposed methodology is highly effective, especially in cases where a large number of harmonics is required. Furthermore, it is optimised at several levels, reaching the maximum possible efficiency. Special concern is given on its implementation on quadratic elements that are of current practice. The method is applicable to any type of boundary elements as well as to a wider class of static and dynamic axisymmetric boundary value problems.

Fourier methods used in two‐ and three‐dimensional image reconstruction can be used also in reconstructability analysis (RA). These methods maximize a variance‐type measure instead of information‐theoretic uncertainty, but the two measures are roughly collinear and the Fourier approach yields results close to that of standard RA. The Fourier method, however, does not require iterative calculations for models with loops. Moreover, the error in Fourier RA models can be assessed without actually generating the full probability distributions of the models; calculations scale with the size of the data rather than the state space. State‐based modeling using the Fourier approach is also readily implemented. Fourier methods may thus enhance the power of RA for data analysis and data mining.

The paper deals with the development of an improved fast Fourier transform (FFT)-based numerical method for computing the effective properties of composite conductors. The convergence of the basic FFT-based methods is recognized to depend drastically on the contrast between the phases. For instance, the primal formulation is not suited for solving the problems with high conductivity whereas the dual formulation is computationally costly for problems with high resistivity. Consequently, it raises the problem of computing the properties of composites containing both highly conductive and resistive inclusions.

In the present work, the authors' propose a new iterative scheme for solving that kind of problems which is formulated in term of the polarization.

The capability and relevance of this iterative scheme is illustrated through numerical implementation in the case of composites containing squared inclusions. It is shown that the rate of convergence is increased and thus, particularly when the case of high contrasts is considered. The predominance of the polarization based iterative scheme (PBIS) over existing ones is also illustrated in the case of a composite containing both highly conductive and highly resistive inclusions.

The method is easy to implement and uses the same ingredients as the basic schemes: the FFT and the exact expression of the Green tensor in the Fourier space. Moreover, its convergence conditions do not depend on the conductivity properties of the constituents, which then constitutes the main difference with other existing iterative schemes. The method can then be applied for computing the effective properties of composites conductors with arbitrary contrasts.

This paper aims to explore a new way to extract the fault feature of a rolling bearing signal on the basis of a combinatorial method.

By combining local mean decomposition (LMD) with Teager energy operator, a new feature-extraction method of a rolling bearing fault signal was proposed, called the LMD–Teager transform method. The principles and steps of method are presented, and the physical meaning of the time–frequency power spectrum and marginal spectrum is discussed. On the basis of comparison with the fast Fourier transform method, a simulated non-stationary signal was processed to verify the effect of the new method. Meanwhile, an analysis was conducted by using the recorded vibration signals which include inner race, out race and bearing ball fault signal.

The results show that the proposed method is more suitable for the non-stationary fault signal because the LMD–Teager transform method breaks through the difficulty of the Fourier transform method that can process only the stationary signal. The new method can extract more useful information and can provide better analysis accuracy and resolution compared with the traditional Fourier method.

Combining the advantage of the local mean decomposition and the Teager energy operator, the LMD–Teager method suits the nature of the fault signal. A marginal spectrum obtained from the LMD–Teager method minimizes the estimation bias brought about by the non-stationarity of the fault signal. So, the LMD–Teager transform has better analysis accuracy and resolution than the traditional Fourier method, which provides a good alternative for fault diagnosis of the rolling bearing.

The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution.

The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes.

Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems.

The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.

The authors proposed a new method of fast time delay measurement for integrated pulsar pulse profiles in X-ray pulsar-based navigation (XNAV). As a basic observation of exact orientation in XNAV, time of arrival (TOA) can be obtained by time delay measurement of integrated pulsar pulse profiles. Therefore, the main purpose of the paper is to establish a method with fast time delay measurement on the condition of limited spacecraft’s computing resources.

Given that the third-order cumulants can suppress the Gaussian noise and reduce calculation to achieve precise and fast positioning in XNAV, the proposed method sets the third-order auto-cumulants of standard pulse profile, the third-order cross-cumulants of the standard and the observed pulse profile as basic variables and uses the cross-correlation function of these two variables to estimate the time delay of integrated pulsar pulse profiles.

The proposed method is simple, fast and has high accuracy in time delay measurement for integrated pulsar pulse profiles. The result shows that compared to the bispectrum algorithm, the method improves the precision of the time delay measurement and reduced the computation time significantly as well.

To improve the performance of time delay estimation in XNAV systems, the authors proposed a novel method for XNAV to achieve precise and fast positioning.

Compared to the bispectrum algorithm, the proposed method can improve the speed and precision of the TOA’s calculation effectively by using the cross-correlation function of integrated pulsar pulse profile’s third-order cumulants instead of Fourier transform in bispectrum algorithm.