• Explosives and Blasting
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• v.23 no.3
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• pp.27-42
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• 2005

An explosion modeling technique was developed by using the spherical discrete element code, $PFC^{3D}$, which can be used to model the dynamic stress wave propagation phenomenon. The modeling technique is simply based on an idea that the explosion pressure should be applied to a $PFC^{3D}$ particle assembly not in the form of an external force (body force), but in the form of a contact force (surface force). The stress wave propagation modeling was conducted by simulating the experimental approach based on the Hopkinson's effect combined with the spatting phenomenon that had previously been developed to determine the dynamic tensile strength of Inada granite. As a result, the stress wave velocity obtained by the proposed modeling technique was 4167 m/s, which is merely $3\%$ lower than the actual wave velocity of 4300 m/s for an Inada granite.

• Geophysics and Geophysical Exploration
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• v.20 no.3
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• pp.129-136
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• 2017

3D seismic data processing methods such as full waveform inversion or reverse-time migration require 3D wave propagation modeling and heavy calculations. We compared efficiency and accuracy of a Xeon Phi coprocessor to those of a high-end server CPU using 3D frequency-domain wave propagation modeling. We adopted the OpenMP parallel programming to the time-domain finite difference algorithm by considering the characteristics of the Xeon Phi coprocessors. We applied the Fourier transform using a running-integration to obtain the frequency-domain wavefield. A numerical test on frequency-domain wavefield modeling was performed using the 3D SEG/EAGE salt velocity model. Consequently, we could obtain an accurate frequency-domain wavefield and attain a 1.44x speedup using the Xeon Phi coprocessor compared to the CPU.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.10a
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• pp.81-88
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• 2000

The elastic wave equation is solved using the finite-difference method in 3D space to simulate the seismic wave propagation. It is based on the velocity-stress formulation of the equation of motion on a staggered grid. The nonreflecting boundary conditions are used to attenuate the wave field close to the numerical boundary. To satisfy the stress-free conditions at the free-surface boundary, a new formulation combining the zero-stress formalism with the vacuum one is applied. The effective media parameters are employed to satisfy the traction continuity condition across the media interface. With use of the moment-tensor components, the wide range of source mechanism parameters can be specified. The numerical experiments are carried out in order to test the applicability and accuracy of this scheme and to understand the fundamental features of the wave propagation under the generalized elastic media structure. Computational results show that the scheme is sufficiently accurate for modeling wave propagation in 3D elastic media and generates all the possible phases appropriately in under the given heterogeneous velocity structure. Also the characteristics of the ground motion in an sedimentary basin such as the amplification, trapping, and focusing of the elastic wave energy are well represented. These results demonstrate the use of this simulation method will be helpful for modeling the ground motion of seismological and engineering purpose like earthquake hazard assessment, seismic design, city planning, and etc..

• Journal of the Korean Society for Nondestructive Testing
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• v.20 no.2
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• pp.138-149
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• 2000

Various modeling techniques for ultrasonic wave propagation and scattering problems in finite solid media are presented. Elastodynamic boundary value problems in inhomogeneous multi-layered plate-like structures are set up for modal analysis of guided wave propagation and numerically solved to obtain dispersion curves which show propagation characteristics of guided waves. As a powerful modeling tool to overcome such numerical difficulties in wave scattering problems as the geometrical complexity and mode conversion, the Boundary Element Method(BEM) is introduced and is combined with the normal mode expansion technique to develop the hybrid BEM, an efficient technique for modeling multi mode conversion of guided wave scattering problems. Time dependent wave forms are obtained through the inverse Fourier transformation of the numerical solutions in the frequency domain. 3D BEM program development is underway to model more practical ultrasonic wave signals. Some encouraging numerical results have recently been obtained in comparison with the analytical solutions for wave propagation in a bar subjected to time harmonic longitudinal excitation. It is expected that the presented modeling techniques for elastic wave propagation and scattering can be applied to establish quantitative nondestructive evaluation techniques in various ways.

• Geophysics and Geophysical Exploration
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• v.22 no.2
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• pp.56-61
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• 2019

In this paper, we studied efficient modeling strategies when we simulate the 3D time-domain acoustic wave propagation using a cell-based finite difference method which can handle the variations of both P-wave velocity and density. The standard finite difference method assigns physical properties such as velocities of elastic waves and density to grid points; on the other hand, the cell-based finite difference method assigns physical properties to cells between grid points. The cell-based finite difference method uses average physical properties of adjacent cells to calculate the finite difference equation centered at a grid point. This feature increases the computational cost of the cell-based finite difference method compared to the standard finite different method. In this study, we used additional memory to mitigate the computational overburden and thus reduced the calculation time by more than 30 %. Furthermore, we were able to enhance the performance of the modeling on several media with limited density variations by using the cell-based and standard finite difference methods together.

• Geophysics and Geophysical Exploration
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• v.20 no.2
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• pp.72-77
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• 2017

We calculated 3D frequency- and Laplace-domain wavefields using time-domain modeling and Fourier transform or Laplace transform. We adopted OpenACC and GPU for an efficient parallel calculation. The OpenACC makes it easy to use GPU accelerators by adding directives in conventional C, C++, and Fortran programming languages. Accordingly, one doesn't have to learn new GPGPU programming languages such as CUDA or OpenCL to use GPU. An OpenACC program allocates GPU memory, transfers data between the host CPU and GPU devices and performs GPU operations automatically or following user-defined directives. We compared performance of 3D wave propagation modeling programs using OpenACC and GPU to that using single-core CPU through numerical tests. Results using a homogeneous model and the SEG/EAGE salt model show that the OpenACC programs are approximately 53 and 30 times faster than those using single-core CPU.

• Geophysics and Geophysical Exploration
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• v.21 no.4
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• pp.213-219
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• 2018

In this study, we simulated 3D wave propagation modeling using a Xeon Phi x200 processor and compared the parallel computation performance with that using a Xeon CPU. Unlike the 1st generation Xeon Phi coprocessor codenamed Knights Corner, the 2nd generation x200 Xeon Phi processor requires no additional communication between the internal memory and the main memory since it can run an operating system directly. The Xeon Phi x200 processor can run large-scale computation independently, with the large main memory and the high-bandwidth memory. For comparison of parallel computation, we performed the modeling using the MPI (Message Passing Interface) and OpenMP (Open Multi-Processing) libraries. Numerical examples using the SEG/EAGE salt model demonstrated that we can achieve 2.69 to 3.24 times faster modeling performance using the Xeon Phi with a large number of computational cores and high-bandwidth memory compared to that using the 12-core CPU.

• Geophysics and Geophysical Exploration
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• v.15 no.2
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• pp.57-65
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• 2012

Various numerical methods in simulation of seismic wave propagation have been developed. Recently an innovative numerical method called as the Spectral Element Method (SEM) has been developed and used in wave propagation in 3-D elastic media. The SEM that easily implements the free surface of topography combines the flexibility of a finite element method with the accuracy of a spectral method. It is generally used a weak formulation of the equation of motion which are solved on a mesh of hexahedral elements based on the Gauss-Lobatto-Legendre integration rule. Variational formulations of velocity-stress motion are newly modified in order to implement ADE-PML (Auxiliary Differential Equation of Perfectly Matched Layer) in wave propagation in 3-D elastic media, because a general weak formulation has a difficulty in adapting CFS (Complex Frequency Shifted) PML (Perfectly Matched Layer). SEM of Velocity-Stress motion having ADE-PML that is very efficient in absorbing waves reflected from finite boundary is verified with simulation of 1-D and 3-D wave propagation.

• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.145-152
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• 2016

We used graphics processing units for an efficient time-domain 3D wave propagation modeling. Since graphics processing units are designed for massively parallel processes, we need to optimize the calculation and memory management to fully exploit graphics processing units. We focused on the memory management and examined the performance of programs with respect to the memory management methods. We also tested the effects of memory transfer on the performance of the program by varying the order of finite difference equation and the size of velocity models. The results show that the memory transfer takes a larger portion of the running time than that of the finite difference calculation in programs transferring whole 3D wavefield.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.18-23
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• 2000

The radar method is becoming one of the major nondestructive testing (NDT) techniques for concrete structures. Numerical modeling of electromagnetic wave is needed to analyze radar measurement results and to study the influence of measurement parameters on the radar measurements. Finite difference-time domain (FD-TD) method is used to simulate electromagnetic wave propagation through concrete specimens. Three concrete specimens with a 19.1 mm rebar embedded at 40 mm, 60 mm, and 80 mm depth are modeled in 3-dimension. As results, 2-D image processing scheme of modeling data has been developed and applied to the imaging of steel bars inside concrete.