Iterative magnetic forward modeling for high susceptibility based on integral equation and Gauss-fast Fourier transform

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. J1-J13 ◽  
Author(s):  
Fang Ouyang ◽  
Longwei Chen
Keyword(s):  
Integral Equation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Extreme Case ◽  
Computational Time ◽  
Acceptable Result ◽  
Iterative Computation ◽  
Wide Range ◽  
Numerical Precision ◽  
Complex Target

Self-demagnetization due to strongly magnetic bodies can seriously affect the interpretation of magnetic anomalies. Conventional numerical methods often neglect the self-demagnetization effects and limit their use to low susceptibilities ([Formula: see text]). We have developed a novel iterative method based on the integral equation and the Gauss-fast Fourier transform (FFT) technique for calculating the magnetic field from finite bodies of high magnetic susceptibility and arbitrary shapes. The method uses a segmented model consisting of prismatic voxels to approximate a complex target region. In each voxel, the magnetization is assumed to be constant, so that the integral equation in the spatial domain can reduce to a simple form with lots of merit in numerical calculation after the 2D Fourier transform. Moreover, a contraction operator is derived to ensure the convergence of the iterative calculation, and the Gauss-FFT technique is applied to reduce numerical errors due to edge effects. Our modeling results indicate that this new iterative scheme performs well in a wide range of magnetic susceptibilities (1–1000 SI). For lower susceptibilities ([Formula: see text]), the iterative algorithm converges rapidly and indicates very good correlation with the analytical solutions. At higher susceptibilities ([Formula: see text]), our method still performs well, but the numerical accuracy improves with a relatively slow speed. In the extreme case ([Formula: see text]), an acceptable result is also obtained after sufficient iterative computation. A further improvement in the numerical precision can be achieved by increasing the number of prismatic voxels, but at the same time, the computational time increases linearly with the size of the voxels.

scholarly journals Flow and Fast Fourier Transform Analyses for Tip Clearance Effect in an Operating Kaplan Turbine

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 264 ◽  
Author(s):  
Hyoung-Ho Kim ◽  
Md Rakibuzzaman ◽  
Kyungwuk Kim ◽  
Sang-Ho Suh
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Tip Clearance Flow ◽  
Kaplan Turbine ◽  
Turbine Performance ◽  
Wide Range ◽  
Clearance Flow ◽  
Fft Analysis

The Kaplan turbine is an axial propeller-type turbine that can simultaneously control guide vanes and runner blades, thus allowing its application in a wide range of operations. Here, turbine tip clearance plays a crucial role in turbine design and operation as high tip clearance flow can lead to a change in the flow pattern, resulting in a loss of efficiency and finally the breakdown of hydro turbines. This research investigates tip clearance flow characteristics and undertakes a transient fast Fourier transform (FFT) analysis of a Kaplan turbine. In this study, the computational fluid dynamics method was used to investigate the Kaplan turbine performance with tip clearance gaps at different operating conditions. Numerical performance was verified with experimental results. In particular, a parametric study was carried out including the different geometrical parameters such as tip clearance between stationary and rotating chambers. In addition, an FFT analysis was performed by monitoring dynamic pressure fluctuation on the rotor. Here, increases in tip clearance were shown to occur with decreases in efficiency owing to unsteady flow. With this study’s focus on analyzing the flow of the tip clearance and its effect on turbine performance as well as hydraulic efficiency, it aims to improve the understanding on the flow field in a Kaplan turbine.

Advanced Control for Clusters of SOFC/Gas Turbine Hybrid Systems

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Iacopo Rossi ◽  
Valentina Zaccaria ◽  
Alberto Traverso
Keyword(s):  
Fuel Cell ◽  
Power Systems ◽  
Gas Turbine ◽  
Power Plants ◽  
Numerical Approach ◽  
Computational Time ◽  
Target System ◽  
Wide Range ◽  
Advanced Control ◽  
Complex Target

The use of model predictive control (MPC) in advanced power systems can be advantageous in controlling highly coupled variables and optimizing system operations. Solid oxide fuel cell/gas turbine (SOFC/GT) hybrids are an example where advanced control techniques can be effectively applied. For example, to manage load distribution among several identical generation units characterized by different temperature distributions due to different degradation paths of the fuel cell stacks. When implementing an MPC, a critical aspect is the trade-off between model accuracy and simplicity, the latter related to a fast computational time. In this work, a hybrid physical and numerical approach was used to reduce the number of states necessary to describe such complex target system. The reduced number of states in the model and the simple framework allow real-time performance and potential extension to a wide range of power plants for industrial application, at the expense of accuracy losses, discussed in the paper.

scholarly journals PRICING HOLDER-EXTENDABLE CALL OPTIONS WITH MEAN-REVERTING STOCHASTIC VOLATILITY

2019 ◽  
Vol 61 (4) ◽  
pp. 382-397
Author(s):  
S. N. I. IBRAHIM ◽  
A. DÍAZ-HERNÁNDEZ ◽  
J. G. O’HARA ◽  
N. CONSTANTINOU
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Stochastic Volatility ◽  
Fourier Method ◽  
Heston Model ◽  
Computational Time ◽  
Characteristic Functions ◽  
Underlying Asset ◽  
Call Options ◽  
Integral Forms

Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls.

scholarly journals Simulation of Memory-Based 1024-Point Fast Fourier Transform for Broadband Wireless Access Technology on FPGA

2017 ◽  
Vol 1 (02) ◽  
pp. 28-36 ◽  
Author(s):  
Dinda Pramanta ◽  
Denny Darlis ◽  
Iswahyudi Hidayat
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Power Efficiency ◽  
Orthogonal Frequency Division Multiplexing ◽  
Wireless Access ◽  
Computational Time ◽  
Broadband Wireless Access ◽  
Access Technology ◽  
Broadband Wireless ◽  
Flip Flop

The limited radio frequency spectrum that can be used for transmission leads to bandwidth and power efficiency being a key requirement in the development of wireless access technology from 3G to 5G today. Data communication technology also requires this as mentioned on high speed network standards such as DSL, WLAN and WMAN with its products ADSL, WiFi and Wimax. In the last few decades we have seen the evolution of the Orthogonal Frequency Division Multiplexing (OFDM) modulation technique used in the technologies mentioned earlier to this day. This technique is regarded as a standard technology for broadband wireless access technology. In hardware implementation, the most preferred by many researchers is the Field Programmable Gate Array chip, as it can be reconfigured. The OFDM technique can be easily implemented because it uses Fast Fourier Transform (FFT) algorithms that are coding and programming capable of reducing the computational time of Discrete Fourier Transform. This paper discusses the implementation of the memory-based 1024-point IFFT / FFT for BWA communications. The design is focused on synthesizing and implementing the system block FFT 1024-point radix-4 using Decimation in Frequency (DIF) method. Implementation for IFFT / FFT 1024-point resource usage slice number 1%, the number of slice flip-flop 1%, the number 4 LUT (Look Up Table) 1%, and the number of IOB 27%. of the FPGA are used.

The Evaluation of an Integral Equation Method for Two-Dimensional Shock-Free Flows

1975 ◽  
Vol 26 (1) ◽  
pp. 59-70 ◽  
Author(s):  
D Nixon ◽  
J Patel
Keyword(s):  
Integral Equation ◽  
Integral Equation Method ◽  
Free Flow ◽  
Equation Method ◽  
Computational Time ◽  
Test Cases ◽  
Two Dimensional ◽  
Exact Methods ◽  
Wide Range ◽  
Steady Shock

SummaryThe numerical aspects of the integral equation method developed by Nixon and Hancock for two-dimensional steady shock-free flow have been rationalised; this numerically refined method is evaluated by calculating the pressure distribution around a wide range of aerofoils. These test cases include aerofoils in supercritical shock-free flow as well as subcritical flow and exact solutions are available for comparison. The computational time in the present method is significantly less than that required by the exact methods. The present results compare satisfactorily with the exact results.

A PARALLEL FAST FOURIER TRANSFORM

1999 ◽  
Vol 10 (05) ◽  
pp. 781-805 ◽  
Author(s):  
SILVIA MORANTE ◽  
GIANCARLO ROSSI ◽  
GAETANO SALINA
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Parallel Computers ◽  
Computational Time ◽  
Fast Fourier Transform Algorithm ◽  
Optimal Result ◽  
Asymptotic Values ◽  
Concrete Realization ◽  
Data Points ◽  
Asymptotic Scaling

In this paper we discuss the general problem of implementing the multidimensional Fast Fourier Transform algorithm on parallel computers. We show that, on a machine with P processors and fully parallel node communications, the optimal asymptotic scaling behavior of the total computational time with the number of data points, N, given in d dimensions by the formula aN/P log (N/P)+bN/P(d-1)/d, can actually be achieved on realistic platforms. As a concrete realization of our strategy, we have produced codes efficiently running on machines of the APE family and on Cray T3E. On the former for asymptotic values of N our codes attain the above optimal result.

The Implementation of Fast Fourier Transform and Coherence Function to Detect the Millimetric Hole on Strip Iron Plate

2020 ◽  
Vol 840 ◽  
pp. 430-437
Author(s):  
Ardi Wiranata ◽  
Ekrar Winata
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Trigger Point ◽  
Coherence Function ◽  
Digital Signal ◽  
Vibration Signal ◽  
Computational Time ◽  
Iron Plate ◽  
The Difference ◽  
Magnitude Squared Coherence

In this study, Fast Fourier Transform (FFT) was used in order to detect bore hole in a structure. FFT is a common method in digital signal processing (DSP) to characterize the frequency emitted by some structure. This method is widely used because of its simplicity. Computational time needed for FFT is relatively lower than another method. The use of FFT to analyze defect in structure is not commonly used since FFT has some weakness for example spatial frequency cannot be extracted to point out the defect location. In this paper, defect was designated as a hole in a strip iron plate with 20 mm in diameter. The strip iron plate was 1 meter long, 38 mm wide and 3 mm thick. This strip iron plate was clamped at one of its ends while the other side is left free. In order to produce vibration signal, impact hammer Bruel Kjaer Type 8202 was used with plastic tip to limit the vibration frequency in to the range of 0 - 1000 Hz. The trigger point was 30 mm from its free end. Three accelerometers were placed series in one line with the trigger point with 300 mm distance of each accelerometer. The position of the hole was varied in three different position. The first position was between trigger point and first accelerometer, between first and second accelerometer and between the second and third accelerometer. The raw signal obtained from the accelerometer was processed by using FFT to understand the mode shape changes in the strip iron plate due to the bore hole. Furthermore, the FFT result was analyzed as function of receiver position to determine the position of hole. The result shows that the frequency characters were different in each case and further analysis by using magnitude-squared coherence function need to be used in order to quantitatively find the difference between FFT result.

Sign in / Sign up

Export Citation Format

Share Document