Objective of numerical relativity is to develop simulation code and relating

1
Numerical relativity lab. course welcome.
Objective of numerical relativity is to develop
simulation code and relating computing tools to
solve problems of general relativity and
relativistic astrophysics.
The word numerical relativity is used for the
simulations which involve dynamical spacetime
evolution, and in which one can not simplify the
Einstein equation using symmetry to avoid
solving constrained dynamics.
Numerical relativity is used in highly non-linear
regime, and generic spacetime for which analytic
method (or approximations) can not be used.
2
Numerical relativity lab. course welcome.
Problems motivated from the importance in
relativistic astrophysics 1. Binary neutron
star merger and subsequnet formation of a
hypermassive neutron star or a black hole. 2.
Binary black hole merger. 3. Black hole neutron
star binary merger, and a massive disk formation.
4. Heavy stellar core collapse to a
proto-neutron or a black hole formation.
(relating to the supernova, or hypernova.) 5.
Dynamical or secular instability of a rapidly
rotating neutron star.
These phenomena are considered as the sources
of Short g-ray burst (1, 3) Long g-ray burst
(4) Gravitational waves (all of the above).
Problems motivated from classical or mathematical
general relativity Critical phenomena. Existenc
e of the solution of Einstein equation.
3
Computing elements in numerical relativity.
Initial data preparation (Elliptic eq.)
Time evolution Einstein-Euler system, or
GRMHD (Hyperbolic eq., also solve Gauge
eq.) Micro physics, (neutrino, radiation,
magnetic field, Realistic EOS) GW extraction,
BH horizon finder
Analysis of the simulated data (GW spectrum,
merger remnant) Visualization
4
Plan for the numerical relativity course
Practical aspects.

• Practically learn skills of the scientific
  computing (and skills of the scientific research)
  from a collaboration for developing numerical
  codes in numerical relativity.
• Those skills may include basic know ledges of
• Operating systems, mainly Unix, and associated
  tools.
• Computing language, FORTRAN90/95, Mathematica,
  (debugger, MPI)
• Graphics and visualization.
• Documentation for the code collaboration.
• Writing a paper (if we could produce a
  substantial results).

• However, the instructor may not have know ledges
  about many of the above.
• Exploit web resources for an easy solution.
• Self-teaching and sharing of knowledge of each
  other are requested.

Always think about what kind of contributions
that you could make.
Instructor's role for these aspects is more for
tutoring and coordination.
5
Plan for the numerical relativity course
class organizaton.

• Roughly 1/4 of the class would be used for
  lecturing theory, physics, math
• and numerical methods necessary for the numerical
  relativity.
• For those who wish to have deep understand of
  the numerical
• relativity would have to go through (many)
  original papers.
• (A list of references should be made. )

1.
Roughly 1/2 of the class would be used for actual
coding practical learning for the computing.
1st stage making the initial data code for a
rapidly rotating compact star. In practice,
refer to some FORTRAN 77 codes (written by me),
develop a code in FORTRAN90/95. (Learning
numerical methods as well as FORTRAN90/95.) 2nd
stage Develop a simulation code following
standard formulations, and/or try more
difficult initial data code.
2.
Roughly 1/4 of the class would be used for status
report of each of you, discussion and
coordination to proceed the code collaboration.
3.
6
Planning of computer simulations.
First of all, one should check that the problem
you are going to solve is (astro)physically (or
scientifically) well motivated or not.
0.
Grasp what kind of physics is involved in the
problem. ex) What kind of physics should be
used in the problem (GR necessary)? What
kind of time/length scales are involved?
Is any simplification/analytic method for the
problem available?
1.
2.
Evaluate if the simulation is the most effective
solution for the problem . ex) usually, it
is difficult to go beyond the dynamical time
scale for the simulations
check if the current computing resources is
enough for our purpose. Software
Hardware Memory, CPU.