|Solving Einstein's Equation Numerically Using Spectral Methods|
|Time：||Fri 10:10-12:00, 11-08 ~ 11-29|
|Instructor：||Lee Lindblom [UC San Diego]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
The use of spectral methods to construct approximate numerical solutions to partial differential equations, including in particular Einstein's equation, will be introduced. A variety of mathematical issues associated with Einstein's equation will be discussed that are needed to make such numerical solutions possible including, symmetric hyperbolic formulations of the equation, appropriate gauge (i.e. coordinate) conditions, constraint damping mechanisms, boundary conditions, etc. Special problems that arise in finding numerical solutions for binary black hole space-times, and in finding numerical solutions on manifolds with non-trivial spatial topologies will be discussed. As time permits, other related topics might be discussed (depending on the interests of the participants), for example the accuracy requirements needed for gravitational wave data analysis on the model waveforms produced by numerical solutions, or the use of spectral methods to solve the relativistic inverse stellar structure problem.
A general knowledge of general relativity theory.