Convergence and stability in numerical relativity

被引:29
作者
Calabrese, G [1 ]
Pullin, J [1 ]
Sarbach, O [1 ]
Tiglio, M [1 ]
机构
[1] Louisiana State Univ, Dept Phys & Astron, Baton Rouge, LA 70803 USA
来源
PHYSICAL REVIEW D | 2002年 / 66卷 / 04期
关键词
D O I
10.1103/PhysRevD.66.041501
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic formulations of Einstein's equations. Here we explicitly show that with several of the discretizations that have been used throughout the years, this procedure leads to nonconvergent schemes. That is, arbitrarily small initial errors are amplified without bound when resolution is increased, independently of the amount of numerical dissipation introduced. The lack of convergence introduced by this instability can be particularly subtle, in the sense that it can be missed by several convergence tests, especially in (3+1)-dimensional codes. We propose tests and methods to analyze convergence that may help detect these situations.
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页数:4
相关论文
共 9 条
[1]   Hamiltonian time evolution for general relativity [J].
Anderson, A ;
York, JW .
PHYSICAL REVIEW LETTERS, 1998, 81 (06) :1154-1157
[2]  
Arnowitt R. L., 1962, GRAVITATION INTRO CU
[3]   Numerical integration of Einstein's field equations [J].
Baumgarte, TW ;
Shapiro, SL .
PHYSICAL REVIEW D, 1999, 59 (02)
[4]  
CALABRESE G, GRQC0205073
[5]  
Gustafsson B., 1995, TIME DEPENDENT PROBL, Vsecond
[6]   Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations [J].
Kidder, LE ;
Scheel, MA ;
Teukolsky, SA .
PHYSICAL REVIEW D, 2001, 64 (06)
[7]   EVOLUTION OF 3-DIMENSIONAL GRAVITATIONAL-WAVES - HARMONIC SLICING CASE [J].
SHIBATA, M ;
NAKAMURA, T .
PHYSICAL REVIEW D, 1995, 52 (10) :5428-5444
[8]   THE UNCONDITIONAL INSTABILITY OF INFLOW-DEPENDENT BOUNDARY-CONDITIONS IN DIFFERENCE APPROXIMATIONS TO HYPERBOLIC SYSTEMS [J].
TADMOR, E .
MATHEMATICS OF COMPUTATION, 1983, 41 (164) :309-319
[9]   Stability of the iterated Crank-Nicholson method in numerical relativity [J].
Teukolsky, SA .
PHYSICAL REVIEW D, 2000, 61 (08)