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Discontinuous Galerkin time domain methods for acoustics and comparison with finite difference time domain methods.

机译：间断Galerkin时域声学方法，并与时域有限差分法进行比较。

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摘要

This thesis describes an implementation of the discontinuous Galerkin finite element time domain (DGTD) method on unstructured meshes to solve acoustic wave equations in heterogeneous media. In oil industry people use finite difference time domain (FDTD) methods to simulate seismic surveys, the first step to explore oil and gas in the earth's subsurface, conducted either in land or sea. The results in this thesis indicate that the first order time shift effect resulting from misalignment between numerical meshes and material interfaces in the DGTD method occurs in the same way as interface errors in the finite difference simulation of wave propagation. This thesis describes two approaches: interface-fitting mesh and local mesh refinement, without modifying the DGTD scheme, to decrease this troublesome effect with verifications of 2D examples. The comparison of the DGTD method on the piecewise linear interface-fitting mesh and the staggered FDTD method both applied to a square-circle model and a 2D dome model in this thesis confirms the fact that the DGTD method can achieve a suboptimal second order convergence rate while the error in the staggered FDTD method is dominated by the first order interface error when the curved material interfaces are presented. I conclude that the DGTD method is more efficient than the staggered FDTD method for the two solutions to have roughly the same accuracy when the accuracy requirement becomes more and more strict and the model becomes more and more complex.
机译：本文介绍了在非结构网格上实现不连续伽勒金有限元时域法（DGTD）的方法，以求解非均匀介质中的声波方程。在石油工业中，人们使用时差有限域（FDTD）方法来模拟地震勘探，这是在陆地或海洋中进行的地下地下油气勘探的第一步。本文的结果表明，DGTD方法中数值网格和材料界面之间未对准引起的一阶时移效应的发生与波传播有限差分模拟中的界面误差相同。本文描述了两种方法：接口拟合网格和局部网格细化，而无需修改DGTD方案，通过验证2D实例来减少这种麻烦的影响。本文对分段线性界面拟合网格上的DGTD方法与交错式FDTD方法应用于方圆模型和2D圆顶模型的比较证实了DGTD方法可以实现次优收敛速度的事实当呈现弯曲材料界面时，交错式FDTD方法的误差主要由一阶界面误差决定。我得出结论，当精度要求变得越来越严格且模型变得越来越复杂时，对于两个解决方案来说，DGTD方法比交错式FDTD方法更有效，从而具有大致相同的精度。

著录项

  • 作者

    Wang, Xin.;

  • 作者单位

    Rice University.;

  • 授予单位 Rice University.;
  • 学科 Applied Mathematics.;Geophysics.
  • 学位 M.A.
  • 年度 2010
  • 页码 73 p.
  • 总页数 73
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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