A pixel-based finite element implementation to estimate effective wave velocity in heterogeneous media

IF 2.2 3区 地球科学 Q2 GEOSCIENCES, MULTIDISCIPLINARY
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引用次数: 0

Abstract

In the present work, we present a 2D pixel-based Finite Element strategy to simulate the elastic wave propagation in heterogeneous media. An assembly-free approach is employed for the stiffness matrix, leveraging a pixel-based structured mesh to reduce the memory required to store computations. Additionally, a diagonal Lumped-Mass matrix technique is utilized to address challenges associated with the inversion and storage of the mass matrix. The Leap-frog integration method, known for its amalgamation of stability, precision, and efficiency, is adopted. The combination of these features is aimed at facilitating massive parallel computations for very large systems with 108 to 109 degrees of freedom. In that sense, the present work can be understood as a first step toward a very efficient massive parallel GPU-based voxel-based Finite Element implementation to treat very large digital images with personal computers. The implementation presented here has been validated against theoretical predictions and analytical results derived from classical wave propagation theory. Finally, the transmission test is simulated in two digital models, one representing a layered medium and another representing a medium with complex microstructue obtained via micro-tomography. For the first model, the results are compared with the so called Bakus average, while, for the second model, the results are compared with the corresponding outcomes acquired through an in-house developed static finite element homogenization implementation.

估算异质介质中有效波速的基于像素的有限元方法
在本研究中,我们提出了一种基于像素的二维有限元策略,用于模拟弹性波在异质介质中的传播。刚度矩阵采用无装配方法,利用基于像素的结构网格来减少存储计算所需的内存。此外,还采用了对角集块质量矩阵技术,以解决与质量矩阵的反演和存储相关的难题。跃迁积分法因其兼具稳定性、精确性和高效性而闻名。这些特点的结合旨在促进具有 108 至 109 个自由度的超大系统的大规模并行计算。从这个意义上说,本研究工作可以被理解为迈向基于 GPU 的高效大规模并行体素有限元实现的第一步,以便使用个人电脑处理超大型数字图像。本文介绍的实现方法已与理论预测和经典波传播理论得出的分析结果进行了验证。最后,在两个数字模型中模拟了传输测试,一个代表层状介质,另一个代表通过微断层扫描获得的具有复杂微结构的介质。对于第一个模型,模拟结果与所谓的 Bakus 平均值进行了比较,而对于第二个模型,模拟结果则与通过内部开发的静态有限元均质化实施获得的相应结果进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Applied Geophysics
Journal of Applied Geophysics 地学-地球科学综合
CiteScore
3.60
自引率
10.00%
发文量
274
审稿时长
4 months
期刊介绍: The Journal of Applied Geophysics with its key objective of responding to pertinent and timely needs, places particular emphasis on methodological developments and innovative applications of geophysical techniques for addressing environmental, engineering, and hydrological problems. Related topical research in exploration geophysics and in soil and rock physics is also covered by the Journal of Applied Geophysics.
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