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Application of local discontinuous Galerkin method to Einstein equations
Cao, Zhoujian1,2; Fu, Pei3; Ji, Li-Wei4,5; Xia, Yinhua3
2019
Source PublicationINTERNATIONAL JOURNAL OF MODERN PHYSICS D
ISSN0218-2718
Volume28Issue:1Pages:26
AbstractFinite difference and pseudo-spectral methods have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is less frequently used in numerical relativity. In this paper, we design a finite element algorithm to solve the evolution part of the Einstein equations. This paper is the second one of a systematic investigation of applying adaptive finite element method to the Einstein equations, especially aiming for binary compact objects simulations. The first paper of this series has been contributed to the constrained part of the Einstein equations for initial data. Since applying finite element method to the Einstein equations is a big project, we mainly propose the theoretical framework of a finite element algorithm together with local discontinuous Galerkin method for the Einstein equations in the current work. In addition, we have tested our algorithm based on the spherical symmetric spacetime evolution. In order to simplify our numerical tests, we have reduced the problem to a one-dimensional space problem by taking the advantage of the spherical symmetry. Our reduced equation system is a new formalism for spherical symmetric spacetime simulation. Based on our test results, we find that our finite element method can capture the shock formation which is introduced by numerical error. In contrast, such shock is smoothed out by numerical dissipation within the finite difference method. We suspect this is partly the reason that the accuracy of finite element method is higher than the finite difference method. At the same time, different kinds of formulation parameters setting are also discussed.
KeywordNumerical relativity Einstein equation gravitational wave
DOI10.1142/S0218271819500147
Language英语
Funding ProjectNSFC[11690023] ; NSFC[11622546]
WOS Research AreaAstronomy & Astrophysics
WOS SubjectAstronomy & Astrophysics
WOS IDWOS:000456013000004
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32144
Collection应用数学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
3.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
4.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China
5.Univ Chinese Acad Sci, Sch Phys Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Cao, Zhoujian,Fu, Pei,Ji, Li-Wei,et al. Application of local discontinuous Galerkin method to Einstein equations[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS D,2019,28(1):26.
APA Cao, Zhoujian,Fu, Pei,Ji, Li-Wei,&Xia, Yinhua.(2019).Application of local discontinuous Galerkin method to Einstein equations.INTERNATIONAL JOURNAL OF MODERN PHYSICS D,28(1),26.
MLA Cao, Zhoujian,et al."Application of local discontinuous Galerkin method to Einstein equations".INTERNATIONAL JOURNAL OF MODERN PHYSICS D 28.1(2019):26.
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