• Geomechanics and Engineering
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• 제18권6호
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• pp.651-659
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• 2019

The IB-SEM numerical method combines the spectral/hp element method and the rigid immersed boundary method. This method avoids the problems of low computational efficiency and errors that are caused by the re-division of the grid when the solids move. Based on the Fourier transformation and the 3D immersed boundary method, the 3D IB-SEM system was established. Then, using the open MPI and the Hamilton HPC service, the computational efficiency was increased substantially. The flows around a cylinder and a sphere were simulated by the system. The surface of the cylinder generates vortices with alternating shedding, and these vortices result in a periodic force acting on the surface of the cylinder. When the shedding vortices enter the flow field behind the cylinder, a recirculation zone is formed. Finally, the three-dimensional pore flow was successfully investigated.

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.513-518
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• 2003

In this paper, we have proved a theorem on Hausdorff summability of Fourier series which generalizes various known results. We prove that if $${\int}_{o}^{t}\;{\mid}{\phi}(u){\mid}\;du=o(t)\;as\;t{\rightarrow}0\; and\;\lim_{n{\rightarrow}{\infty}}{\int}^{\eta}_{{\pi}/n}{\frac{{\mid}{\phi}(t)-{\phi}(t+{\pi}/n){\mid}}{t}}dt=o(n)$$ where 0 < ${\eta}$ < 1, then the Fourier series is (H, ${\mu}_n$) summable to s at t = x where the sequence ${\mu}_n$ is given by ${\mu}_n={\int}^1_0x^n{\chi}(x)\;dx\;n=0,1,2\;and\;K_n(t)=\limits\sum_{{\nu}=0}^n(\array {n\\{\nu}})({\Delta}^{{n}-{\nu}}{\mu}_{\nu}){\frac{sin{\nu}t}{t}}$.

• 대한수학회보
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• 제39권4호
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• 소음진동
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• 제4권2호
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Communications for Statistical Applications and Methods
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• 제29권1호
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• pp.127-150
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• 2022

We discuss multiple change-point estimation as edge detection in piecewise smooth functions with finitely many jump discontinuities. In this paper we propose change-point estimators using concentration kernels with Fourier coefficients. The change-points can be located via the signal based on Fourier transformation system. This method yields location and amplitude of the change-points with refinement via concentration kernels. We prove that, in an appropriate asymptotic framework, this method provides consistent estimators of change-points with an almost optimal rate. In a simulation study the proposed change-point estimators are compared and discussed. Applications of the proposed methods are provided with Nile flow data and daily won-dollar exchange rate data.

• Bulletin of the Korean Chemical Society
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• 제32권10호
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• pp.3551-3552
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• 2011

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1999년도 추계종합학술대회 논문집
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• pp.173-176
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• 1999

Frequency responses of the surface acoustic wave(SAW) filters are simulated by using the impulse modeling. The simulation technique of the SAW filters is to use the Fourier transformation to make a correspondence between the impulse response of the filter and the taps in the delay line. Since the Fourier series must be truncated after a finite number of terms, window functions are often used to weight the coefficients to obtain the desirable side-lobe level and bandwidth. The filter design is operated through the iterative simulation procedures. The design process is capable of yielding filters with optimized frequency response characteristics.

• Applied Microscopy
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• 제34권4호
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• pp.211-221
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• 2004

물질을 이루고 있는 원자의 집합체에서 단 한번의 회절이 일어나는 경우의 회절이론의 개발을 소개하였다. Fourier transform으로 이루어지는 역 격자 공간에서의 역격자 공간 분포와 실 공간에서의 패터슨 함수와의 관계를 유도하고 이어 여러 가지 물질을 예로 들어 고찰하였다.

• Interaction and multiscale mechanics
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• 제3권1호
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• pp.81-94
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• 2010

The steady state response of a rotating generalized thermoelastic solid to a moving point load has been investigated. The transformed components of displacement, force stress and temperature distribution are obtained by using Fourier transformation. These components are then inverted and the results are obtained in the physical domain by applying a numerical inversion method. The numerical results are presented graphically for a particular model. A particular result is also deduced from the present investigation.

• Earthquakes and Structures
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• 제9권2호
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• pp.305-320
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• 2015

The present paper is devoted to study SH-wave propagation in heterogeneous layer laying over an inhomogeneous isotropic elastic half-space. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the upper layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-wave increases with the increase of inhomogeneity parameter.