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Simulation of Seismic Wave Propagation and Amplification

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High-Performance Computing for Structural Mechanics and Earthquake/Tsunami Engineering

Part of the book series: Springer Tracts in Mechanical Engineering ((STME))

Abstract

Large scale simulation of ground motion is a vital tool in engineering seismology and earthquake engineering. Need for high performance computing cannot be underestimated, because increasing the spatial resolution results in computing higher frequency components of ground motion which influence structure response. This chapter explains improvement of discretization for large scale simulation of ground motion simulation based on finite element method. Better mathematical treatment is needed for ground motion simulation since it solves a four-dimensional linear or non-linear wave equation so that mass matrix becomes diagonal. Diagonalization of the mass matrix is achieved by utilizing a set of orthogonal and discontinuous basis functions. While it sounds odd, the use of discontinuous basis functions provides us a larger capability of modeling. As examples of large scale simulation of ground motion, the use of K computer, the best supercomputer in Japan in the year of 2015, is explained. A non-linear finite element method is developed in K computer, so that a model of 10,000,000,000 degree-of-freedom is analyzed with 100,000 time steps in less than a half day. Numerical computation techniques and parallel computation enhancement are explained to realize this simulation, which leads to high scalability of the developed finite element method. As an illustrative example, Tokyo Metropolis is used as a target, and a K computer simulation of ground motion ispresented.

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Notes

  1. 1.

    An imaginary Japanese Earth guardian, supported by prayers for peace.

  2. 2.

    Defined as:

    $$\displaystyle\begin{array}{rcl} \text{communication}& =& \text{AVG}\{\mathrm{MPI{\_}Isend + MPI{\_}Irecv} {}\\ & & +\mathrm{MPI{ \_}Allreduce(total)} -\mathrm{MPI{\_}Allreduce(wait)}\} + \mathrm{MIN}\{\mathrm{MPI{\_}Waitall}\}, {}\\ \text{synchronization}& =& \text{AVG}\{\mathrm{MPI{\_}Allreduce(wait)} + \mathrm{MPI{\_}Waitall}\} -\text{MIN}\{\mathrm{MPI{\_}Waitall}\}, {}\\ \text{computation}& =& \text{AVG}\{\mathrm{total}\} -\text{communication} -\text{synchronization}. {}\\ \end{array}$$

    Here, AVG and MIN indicate the average and minimum values of all the compute nodes, respectively. MPI_Barrier is not used.

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Authors and Affiliations

  1. Earthquake Research Institute, The University of Tokyo, Tokyo, Japan

    Muneo Hori & Tsuyoshi Ichimura

  2. Advanced Institute for Computational Science, RIKEN, 7-1-26 Minatoshima Minamimachi, Chuo-ku, Hyogo, 650-0047, Japan

    Kohei Fujita

Authors
  1. Muneo Hori
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  2. Tsuyoshi Ichimura
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  3. Kohei Fujita
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Correspondence to Muneo Hori .

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Editors and Affiliations

  1. Department of Systems Innovation, School of Engineering, The University of Tokyo, Tokyo, Japan

    Shinobu Yoshimura

  2. Earthquake Research Institute, The University of Tokyo, Tokyo, Japan

    Muneo Hori

  3. Department of Architecture and Architectural Engineering, Kyoto University, Kyoto, Kyoto, Japan

    Makoto Ohsaki

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Hori, M., Ichimura, T., Fujita, K. (2016). Simulation of Seismic Wave Propagation and Amplification. In: Yoshimura, S., Hori, M., Ohsaki, M. (eds) High-Performance Computing for Structural Mechanics and Earthquake/Tsunami Engineering. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-21048-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-21048-3_2

  • Publisher Name: Springer, Cham

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