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Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation
Lyu, Chao1,2; Capdeville, Yann1; Zhao, Liang2
2020
Source PublicationGEOPHYSICS
ISSN0016-8033
Volume85Issue:1Pages:T33-T43
AbstractThe spectral element method (SEM) has gained tremendous popularity within the seismological community to solve the wave equation at all scales. Classic SEM applications mostly rely on degrees 4-8 elements in each tensorial direction. Higher degrees are usually not considered due to two main reasons. First, high degrees imply large elements, which make the meshing of mechanical discontinuities difficult. Second, the SEM's collocation points cluster toward the edge of the elements with the degree, degrading the time-marching stability criteria and imposing a small time step and a high numerical cost. Recently, the homogenization method has been introduced in seismology. This method can be seen as a preprocessing step before solving the wave equation that smooths out the internal mechanical discontinuities of the elastic model. It releases the meshing constraint and makes use of very high degree elements more attractive. Thus, we address the question of memory and computing time efficiency of very high degree elements in SEM, up to degree 40. Numerical analyses reveal that, for a fixed accuracy, very high degree elements require less computer memory than low-degree elements. With minimum sampling points per minimum wavelength of 2.5, the memory needed for a degree 20 is about a quarter that of the one necessary for a degree 4 in two dimensions and about one-eighth in three dimensions. Moreover, for the SEM codes tested in this work, the computation time with degrees 12-24 can be up to twice faster than the classic degree 4. This makes SEM with very high degrees attractive and competitive for solving the wave equation in many situations.
DOI10.1190/GEO2019-0087.1
Funding OrganizationNational Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council
WOS KeywordNONPERIODIC HOMOGENIZATION ; FINITE-DIFFERENCE ; ADJOINT METHODS ; FORM INVERSION ; PROPAGATION ; TOMOGRAPHY ; DISPERSION ; MEDIA
Language英语
Funding ProjectNational Natural Science Fund for Distinguished Young Scholars in China[41625016] ; French National Research Agency[ANR-16-CE31-0022-01] ; China Scholarship Council[201804910289]
Funding OrganizationNational Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; National Natural Science Fund for Distinguished Young Scholars in China ; French National Research Agency ; French National Research Agency ; French National Research Agency ; French National Research Agency ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council ; China Scholarship Council
WOS Research AreaGeochemistry & Geophysics
WOS SubjectGeochemistry & Geophysics
WOS IDWOS:000506219100046
PublisherSOC EXPLORATION GEOPHYSICISTS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.iggcas.ac.cn/handle/132A11/95858
Collection岩石圈演化国家重点实验室
Corresponding AuthorLyu, Chao
Affiliation1.Univ Nantes, CNRS, Lab Planetol & Geodynam Nantes, Beijing 100029, Peoples R China
2.Chinese Acad Sci, Inst Geol & Geophys, State Key Lab Lithospher Evolut, Beijing 100029, Peoples R China
First Author AffilicationState Key Laboratory of Lithospheric Evolution
Corresponding Author AffilicationState Key Laboratory of Lithospheric Evolution
Recommended Citation
GB/T 7714
Lyu, Chao,Capdeville, Yann,Zhao, Liang. Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation[J]. GEOPHYSICS,2020,85(1):T33-T43.
APA Lyu, Chao,Capdeville, Yann,&Zhao, Liang.(2020).Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation.GEOPHYSICS,85(1),T33-T43.
MLA Lyu, Chao,et al."Efficiency of the spectral element method with very high polynomial degree to solve the elastic wave equation".GEOPHYSICS 85.1(2020):T33-T43.
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