Finite differences on minimal grids

Author:

Magnier Sophie‐Adélade1,Mora Peter1,Tarantola Albert1

Affiliation:

1. Institut de Physique de Globe de Paris, 75252 Paris Cedex 05, France

Abstract

Conventional approximations to space derivatives by finite differences use orthogonal grids. To compute second‐order space derivatives in a given direction, two points are used. Thus, 2N points are required in a space of dimension N; however, a centered finite‐difference approximation to a second‐order derivative may be obtained using only three points in 2-D (the vertices of a triangle), four points in 3-D (the vertices of a tetrahedron), and in general, N + 1 points in a space of dimension N. A grid using N + 1 points to compute derivatives is called minimal. The use of minimal grids does not introduce any complication in programming and suppresses some artifacts of the nonminimal grids. For instance, the well‐known decoupling between different subgrids for isotropic elastic media does not happen when using minimal grids because all the components of a given tensor (e.g., displacement or stress) are known at the same points. Some numerical tests in 2-D show that the propagation of waves is as accurate as when performed with conventional grids. Although this method may have less intrinsic anisotropies than the conventional method, no attempt has yet been made to obtain a quantitative estimation.

Publisher

Society of Exploration Geophysicists

Subject

Geochemistry and Petrology,Geophysics

Cited by 33 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3