Comparison between Vortex-In-Cell and Vortex Particle Methods on Two-Dimensional Problem

The Fast Fourier Transform (FFT) method for solving the 1-D heat diffusion equation offers an efficient approach for resolving partial differential equations (PDEs) with various time steps . FFT is used to transform the 1-D heat diffusion equation into the frequency domain and back to the time domain through inverse FFT. Using mathematical modeling with initial and Dirichlet boundary conditions, the numerical solutions produced by FFT are compared with analytical solutions. The accuracy of the method is validated using MAE and MSE calculated in Matlab. At several time intervals , the obtained MAE and MSE values indicate a good agreement between the numerical and analytical solutions, with very small errors. Numerical stability analysis confirms the reliability of the FFT method across various The variation in time step has a significant impact on the accuracy and stability of the solution. Smaller time steps improve accuracy and stability but require longer computation times. The optimal time step selected in this study is Increasing the number of discretization points also enhances accuracy but implies an increase in computational load and memory usage. The FFT method demonstrates good numerical consistency with increasing

Central Java Province is a potential area that has an important role in national food production. El Nino and La Nina events have a very large impact if they occur in Indonesia, especially in Central Java Province. This study aims to analyze the impact of El Nino and La Nina events specifically in Central Java Province where the areas more dominantly affected by El Nino and La Nina. The research location uses 3 rainfall stations, namely the Tunggal Wulung Meteorological Station, Tegal Maritime Meteorological Station, and Tanjung Emas Maritime Meteorological Station. The method used is the Fast Fourier Transform (FFT) method and the long periodogram. The results showed that the periods of El Nino and La Nina phenomena recurring using the FFT method are forecasts for the periods 2.2428, 2.8036, and 3.7381 years. While using the lom periodogram method, namely in the periods of 2,480, 2,621, and 3:16 years. The results of the analysis of the FFT method obtained results that varied in the height of rainfall at the 3 stations, while the results of the analysis using the periodogram log showed that the Tunggal Wulung rain station had the highest peak rainfall. This study concludes that there are variations in the peak incidence using either the slow periodogram or the FFT method. However, both of these methods and based on the BMKG and TRMM, the Tunggal Wulung Meteorological Station has the highest peak between Tegal Station and Tanjung Emas Station.

Effect of aggregate shapes on local fields in 3D mesoscale simulations of the concrete creep behavior

As an efficient non-destructive testing method, magnetic flux leakage (MFL) has been widely used for damage detection in ferromagnetic materials. The magnetic dipole theory is a traditional method to calculate the magnetic leakage field. In this paper, the magnetic leakage field functions of a slot in a 2-D infinity plate are obtained using the magnetic dipole theory. Equations of the magnetic leakage field are converted into the convolution of two other functions. Spatial spectral equations of the MFL are developed according to the convolution theorem using the Fourier transform (FT) method. The results are analytical functions different from other numerical methods, such as the discrete FT and fast FT methods, and the calculation speed is fast. The results show that the y-component of the magnetic leakage field has 90° phase shift with the x-component. This result has clear physical significance compared with the traditional MFL equations using the magnetic dipole theory. Different spatial spectral curves for different defects are presented in this paper. Since there is a sinc function for the width value in the equation, the width value can be deduced from the first zero-crossing point in the spatial spectrum curves. A new method is proposed to determine the width value using the relationship w =1/f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , where f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> is the first zero cross point. Two specimens with different cracks are investigated, and the experimental results show this method can be used as an inverse MFL data interpretation technique.

Rotor wake causes unsteady aerodynamics of rotor blade. So, accurate prediction of wake is very important and vortex method is good solution for this problem. Aerodynamic force of the rotor blade is calculated by potential panel method and the rotor wake is simulated by vortex particle method. The vortex particle method is easier to treat wake-body interaction and has better performance to expect the effect of ground and fuselage interaction. Rotor in hovering and forward flight condition is simulated through these methods. Thrust and surface pressure of rotor are compared with experiment data.

Maximum Entropy Spectral Analysis (MESA) Method is a powerful alternative to the traditionally used Blackman Tukey (BT) and Fast Fourier Transform (FFT) Methods in hydrologic and climatologic time series analysis. Maximum entropy spectra of annual rainfall time series measured at Mangalore and Waltair and monthly flow time series of Godavari and Krishna Rivers in India are presented and compared with the spectra obtained by using BT and FFT methods. A recently developed Bayesian decision rule is applied to determine the length of filters in MESA. Sensitivity of the maximum entropy spectra to the length of filter used is also discussed.

Eddy current nondestructive evaluation (NDE) of airframe structures involves the detection of electromagnetic field irregularities due to non-conducting inhomogeneities in an electrically conducting material. Usually, the eddy current NDE problem can be formulated by the boundary integral equations (BIE) and discretized into matrix equations by the method of moments (MoM) or the boundary element method (BEM). The fast multipole method (FMM) is a well-established and effective method for accelerating numerical solutions of the matrix equations. Accelerated by the FMM, the BIE method can now solve large-scale electromagnetic wave propagation and diffusion problems. The traditional BIE method requires O(N) operations to compute the system of equations and another O(N) operations to solve the system using direct solvers, with N being the number of unknowns; in contrast, the BIE method accelerated by the two-level FMM can potentially reduce the operations and memory requirement to O(N). Moreover, several approaches have been proposed for the field calculation in the presence of flaws in three dimensional NDE; however, seldom work has been done in applying efficient methods to seek rapid solution in eddy current NDE simulation. As elaborated in the dissertation, we introduce a fast multipole BIE method for two-dimensional diffusive scalar problem and an efficient BIE method for three-dimensional eddy current NDE. Firstly, we work with the two-dimensional Helmholtz equation with a complex wave number for non-trivial boundary geometry. We describe the FMM acceleration procedure of the BIE method and its features briefly, explaining that the FMM is not only efficient in meshing complicated geometries, accurate for solving singular fields or

Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method.

The discrete vortex method has been used for incompressible high Reynolds number flows as a simple numerical simulation method. Ohgami and Akamatsu proposed the viscous diffusion model, and applied the vortex method to simulate viscous flow. In this study, we estimate the accuracy of this model both mathematically and numerically, and then show the computational procedures of this method for the case of application to an arbitrarily shaped body. In the discrete vortex method, the surface pressure distribution is calculated conventionally from the unsteady Bernoulli equation, but it is not available for viscous flow. We propose a simple method based on the boundary element method to calculate the pressure distribution for the discrete vortex method with the viscous diffusion model.

Discussion: “Three-Dimensional Vortex Method for Gas-Particle Two-Phase Compound Round Jet” (Uchiyama, T., and Fukase, A., 2005, ASME J. Fluids Eng., 127, pp. 32–40)

Interferometric instruments have the following serious weak points: (1) the necessity of doing a Fourier transform that involves a vast amount of calculation; (2) the lack of knowledge of suitable measuring conditions until the Fourier transform is finished; and (3) the spectral resolution of the conventional Fourier-based techniques is significantly affected by the sampling rate, data length, and noise in signal processing. In this paper, an enhanced spectrometer is proposed using the modified forward-backward linear prediction method (MFBLP) with a search algorithm. To document the advantage of the method presented, a computer simulation for multiple-wavenumber estimation is investigated. The MFBLP method is truly superior to the fast Fourier transform (FFT) method. In general, the spectral resolution using the FFT method is proportional to the data length. In this paper, however, it is shown that excellent results can also be obtained from only 60 sample points using the FFT method. Moreover, from experimental results, we also conclude that the sampling rate must be consistent with the condition 632<f/sub p//spl middot/t/spl middot/D<3164, where f/sub p/, represents the value of the pulse generator frequency in Hz, t the observation time, and D the decimation factor.

This paper introduces parallel computation for spread options using two-dimensional Fourier transform. Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial securities. Pricing these securities, however, cannot be done using closed-form methods; as such, we propose an algorithm which employs the fast Fourier Transform (FFT) method to numerically solve spread option prices in a reasonable amount of short time while preserving the pricing accuracy. Our results indicate a significant increase in computational performance when the algorithm is performed on multiple CPU cores and GPU. Moreover, the literature on spread option pricing using FFT methods documents that the pricing accuracy increases with FFT grid size while the computational speed has opposite effect. By using the multi-core/GPU implementation, the trade-off between pricing accuracy and speed is taken into account effectively.

Chapter 6 - Fast Fourier transform methods

The fast Fourier transform (FFT) algorithm is widely used as a standard tool to carry out spectral analysis because of its computational efficiency. However, the presence of multiple tones frequently requires a fine frequency resolution to achieve sufficient accuracy, which imposes the use of a large number of FFT points that results in large area and power overheads. In this paper, an FFT method is proposed for on-chip spectral analysis of multi-tone signals with particular harmonic and intermodulation components. This accurate FFT analysis approach is based on coherent sampling, but it requires a significantly smaller number of points to make the FFT realization more suitable for on-chip built-in testing and calibration applications that require area and power efficiency. The technique was assessed by comparing the simulation results from the proposed method of single and multiple tones with the simulation results obtained from the FFT of coherently sampled tones. The results indicate that the proper selection of test tone frequencies can avoid spectral leakage even with multiple narrowly spaced tones. When low-frequency signals are captured with an analog-to-digital converter (ADC) for on-chip analysis, the overall accuracy is limited by the ADC's resolution, linearity, noise, and bandwidth limitations. Post-layout simulations of a 16-point FFT showed that third-order intermodulation (IM3) testing with two tones can be performed with 1.5-dB accuracy for IM3 levels of up to 50 dB below the fundamental tones that are quantized with a 10-bit resolution. In a 45-nm CMOS technology, the layout area of the 16-point FFT for on-chip built-in testing is 0.073 mm2, and its estimated power consumption is 6.47 mW.

To apply both autoregressive (AR) and fast Fourier transform (FFT) spectral analysis at rest, during two different dynamic exercise intensities and in recovery from maximal exercise and to compare raw and normalized powers obtained with both methods. Sixteen participants (age 22.3 +/- 4.3 year) performed resting, submaximal and maximal protocols. The submaximal protocol consisted of two 5-min walks at 4 km h(-1) at treadmill grades of 0 and 7.5%. Beat-to-beat R-R series were recorded. FFT and AR analyses were preformed on the same R-R series. Compared to AR, FFT provided higher total power (TP) and raw high-frequency (HF) power at rest and exercise. Furthermore, FFT LF/HF ratio was lower than with the AR, except under resting conditions. Both methods showed reductions in TP, raw HF and LF powers during exercise and recovery. Only the AR revealed a significant reduction for normalized HF power and increase for normalized LF power in transition from rest to exercise conditions. AR and FFT methods are not interchangeable at rest or during dynamic exercise conditions. The AR method is more sensitive to the effects of exercise on the normalized power spectra of heart rate variability (HRV) than FFT. Finally, as both approaches are equally insensitive to the increase of exercise relative intensity, there is no practical advantage of performing HRV spectral analyses by the AR or FFT at higher workloads.