Journal article
A robust method of computing finite difference coefficients based on Vandermonde matrix
Journal of applied geophysics, Vol.152, pp.110-117
05/2018
DOI: 10.1016/j.jappgeo.2018.03.013
Abstract
When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB.
•FD coefficients computed by matrix inverse operator of MATLAB induce inaccuracy.•An algorithm based on Vandermonde matrix is suggested to compute FD coefficients.•Dispersion curves and numerical results show robustness of the proposed algorithm.
Details
- Title: Subtitle
- A robust method of computing finite difference coefficients based on Vandermonde matrix
- Creators
- Yijie Zhang - Xi'an Jiaotong UniversityJinghuai Gao - Xi'an Jiaotong UniversityJigen Peng - Xi'an Jiaotong UniversityWeimin Han - Xi'an Jiaotong University
- Resource Type
- Journal article
- Publication Details
- Journal of applied geophysics, Vol.152, pp.110-117
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.jappgeo.2018.03.013
- ISSN
- 0926-9851
- eISSN
- 1879-1859
- Grant note
- DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 41704126; DOI: 10.13039/501100002858, name: China Postdoctoral Science Foundation, award: 2017M613105; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 41390450, 41390454; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 91730306
- Language
- English
- Date published
- 05/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984241159202771
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