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Jan 13, 2000
Our View of the "Important Problems"
M. Alcubierre, T. Baumgarte, G. Cook, L. Kidder, M. Scheel
The following is an outline of a few of the important
impeding work on numerical simulations of binary coalescence. We hope
will promote some useful discussion. There are certainly other
but these are the problems we think should be tackled first and which
benefit from theoretical analysis.
When your simulation blows
- Gauge Modes
- Grid sucking, coordinate shocks, focusing, grid
- Constraint Violating Modes
- Solutions of the continuum evolution equations
ill-behaved away from the constraint
- Numerical Instabilities
- Solutions of the numerical
that are ill-behaved.
When our simulations blow up, what needs to be fixed? We have several
that the continuum evolution equations are at fault and we would like
more general framework for understanding which systems of evolution
Constraint violating modes
- Examples using seemingly reasonable sets of
- Alcubierre's analysis of why "Conformal ADM"
- Scheel's analysis of how the constraints can be used in 1D
- How do we analyze/recognize these problems?
- We have some simplified, linear
- We really need some more
Points that should be kept in mind when studying the
of evolution schemes.
- Well-posedness is not enough:
- It only guarantees that errors grows no faster
- The principal part isn't the only source of
- Perturbative analyses should be done about
than flat space or Schwarzschild coordinates.
- How does choice of background (slicing) affect
It seems clear that stability may depend strongly on the gauge
to evolve the system. Can we make any statements about the classes of
or shift conditions within which a given evolution scheme is
- This really means we need to know what coordinates
to keep out of trouble.
- What boundary conditions do we use on elliptic
conditions at excision boundaries?
- What gauge conditions drive us to
at late time?
- How do we extract information from the solution
us how to place the coordinates?
While we have separated constraint violating modes and
it isn't clear that they can be analyzed independently.
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