• Geomechanics and Engineering
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• v.13 no.3
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• pp.411-429
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• 2017

A Spectral Element Method for 3D seismic wave propagation simulation is derived based on the three-dimensional fluctuating elastic dynamic equation. Considering the 3D real terrain and the attenuation characteristics of the medium, the topographic effect of Wenchuan earthquake is simulated by using the Spectral Element Method (SEM) algorithm and the ASTER DEM model. Results show that the high PGA (peak ground acceleration) region was distributed along the peak and the slope side away from the epicenter in the epicenter area. The overall distribution direction of high PGA and high PGV (peak ground velocity) region is parallel to the direction of the seismogenic fault. In the epicenter of the earthquake, the ground motion is to some extent amplified under the influence of the terrain. The amplification effect of the terrain on PGA is complicated. It does not exactly lead to amplification of PGA at the ridge and the summit or attenuation of PGA in the valley.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.359-373
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• 2012

The block LU factorization is used to solve the coupled Stokes equations arisen from an optimal control problem subject to Stokes equations. The convergence of the spectral element solution is proved. Some numerical evidences are provided for the model coupled Stokes equations. Moreover, as an application, this algorithm is performed for an optimal control problem.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.382-385
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• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved fly using the high-order spectral method and body potential is solved fly using the high-order boundary element method. Through the combination of these two methods, the wave-making problems fly a submerged sphere moving with the large amplitude oscillation are solved in time-domain. With the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Proceedings of the KSR Conference
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• 2009.05a
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• pp.1092-1096
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• 2009

The spectral element modeling is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model with variational method for an axially moving string subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is the verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving string are investigated.

• Journal of Korean Society for Atmospheric Environment
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• v.9 no.3
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• pp.242-246
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• 1993

Theoretically, spectral method has the highest accuracy among present numerical methods, but it is generally difficult to apply to complex terrains because of complex boundary conditions. Recently, spectral-element method, basically divide the domain into a set of rectangular subdomain and solve the equation at each subdomain, has been introduced. However, boundary conditions become more complex and requires more computing time, thus spectral-element method is not powerful for all complex terrain problems. In this paper, potential flow theory was intorduced to solve the air flows and diffusion phenomenon in the presence of terrain obstacles. Using the velocity potential-stream line orthogonal coordinate space, the diffusion problems of hilly terrain by pseudospectral method were solved and compared those with no terrain real scale solutions.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.113-120
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• 1999

In this paper, mathematical formulation of the high-order spectral/boundary-element method is shown. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated in time-domain. Three-dimensional waves generated by a uniformly translating suriace pressure are calculated and discussed. The obtained results are compared with others results, The comparisons show good agreements.

• Earthquakes and Structures
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• v.3 no.3_4
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• pp.383-411
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• 2012

The objective of the present paper is to review and implement the most recent developments in the Spectral Element Method (SEM), as well as improve aspects of its implementation in the study of wave propagation by numerical simulation in elastic unbounded domains. The classical formulation of the method is reviewed, and the construction of the mass matrix, stiffness matrix and the external force vector is expressed in terms of matrix operations that are familiar to earthquake engineers. To account for the radiation condition at the external boundaries of the domain, a new absorbing boundary condition, based on the Perfectly Matched Layer (PML) is proposed and implemented. The new formulation, referred to as the Multi-Axial Perfectly Matched Layer (M-PML), results from generalizing the classical Perfectly Matched Layer to a medium in which damping profiles are specified in more than one direction.

• Geomechanics and Engineering
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• v.1 no.2
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• pp.121-142
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• 2009

The paper deals with the applications of spectral finite element method to the dynamic analysis of framed foundations supporting high speed machines. Comparative performance of approximate dynamic stiffness methods formulated using static stiffness and lumped or consistent or average mass matrices with the exact spectral finite element for a three dimensional Euler-Bernoulli beam element is presented. The convergence of response computed using mode superposition method with the appropriate dynamic stiffness method as the number of modes increase is illustrated. Frequency proportional discretisation level required for mode superposition and approximate dynamic stiffness methods is outlined. It is reiterated that the results of exact dynamic stiffness method are invariant with reference to the discretisation level. The Eigen-frequencies of the system are evaluated using William-Wittrick algorithm and Sturm number generation in the $LDL^T$ decomposition of the real part of the dynamic stiffness matrix, as they cannot be explicitly evaluated. Major's method for dynamic analysis of machine supporting structures is modified and the plane frames are replaced with springs of exact dynamic stiffness and dynamically flexible longitudinal frames. Results of the analysis are compared with exact values. The possible simplifications that could be introduced for a typical machine induced excitation on a framed structure are illustrated and the developed program is modified to account for dynamic constraint equations with a master slave degree of freedom (DOF) option.

• Journal of the Society of Naval Architects of Korea
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• v.46 no.2
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• pp.155-164
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• 2009

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.438-443
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• 1998

In this paper, the axial-bending coupled equations of motion for an elastic layered beam are derived. From this equation of motion, the spectral element is formulated for the vibration analysis by use of the spectral element method (SEM). The modal analysis methodology for the present coupled field equations of motion is then developed. As an illustrative example, a cantilevered beam is considered. The correctness of the equations of motion developed herein is verified by gradually reducing the thickness of upper elastic layer to converge to the single layered elastic beam solutions. Also, the accuracy of spectral element is confirmed by comparing its results with the result by modal analysis.