Abstract
In order to obtain stable and accurate general relativistic simulations, reformulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for evaluating violation behaviour of constraints. In this letter, we classify asymptotical behaviours of constraint violation into three types (asymptotically constrained, asymptotically bounded and diverge), and give their necessary and sufficient conditions. We find that degeneracy of eigenvalues sometimes leads constraint evolution to diverge (even if its real part is not positive) and conclude that it is quite useful to check the diagonalizability of constraint propagation matrices. The discussion is general and can be applied to any numerical treatments of constrained dynamics.
| Original language | English |
|---|---|
| Journal | Classical and Quantum Gravity |
| Volume | 20 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2003 Feb 21 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Diagonalizability of constraint propagation matrices. / Yoneda, Gen; Shinkai, Hisa Aki.
In: Classical and Quantum Gravity, Vol. 20, No. 4, 21.02.2003.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Diagonalizability of constraint propagation matrices
AU - Yoneda, Gen
AU - Shinkai, Hisa Aki
PY - 2003/2/21
Y1 - 2003/2/21
N2 - In order to obtain stable and accurate general relativistic simulations, reformulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for evaluating violation behaviour of constraints. In this letter, we classify asymptotical behaviours of constraint violation into three types (asymptotically constrained, asymptotically bounded and diverge), and give their necessary and sufficient conditions. We find that degeneracy of eigenvalues sometimes leads constraint evolution to diverge (even if its real part is not positive) and conclude that it is quite useful to check the diagonalizability of constraint propagation matrices. The discussion is general and can be applied to any numerical treatments of constrained dynamics.
AB - In order to obtain stable and accurate general relativistic simulations, reformulations of the Einstein equations are necessary. In a series of our works, we have proposed using eigenvalue analysis of constraint propagation equations for evaluating violation behaviour of constraints. In this letter, we classify asymptotical behaviours of constraint violation into three types (asymptotically constrained, asymptotically bounded and diverge), and give their necessary and sufficient conditions. We find that degeneracy of eigenvalues sometimes leads constraint evolution to diverge (even if its real part is not positive) and conclude that it is quite useful to check the diagonalizability of constraint propagation matrices. The discussion is general and can be applied to any numerical treatments of constrained dynamics.
UR - http://www.scopus.com/inward/record.url?scp=0037276533&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037276533&partnerID=8YFLogxK
U2 - 10.1088/0264-9381/20/4/102
DO - 10.1088/0264-9381/20/4/102
M3 - Article
VL - 20
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
SN - 0264-9381
IS - 4
ER -