Solving Einstein's Equations for Binary Black Hole Spacetimes

Comparing Different Numerical Methods
Wave propagation with second-order finite difference method:
3.0
3.0
3.0
N=200
N=200
N=200
2.5
t=0.0
2.5
t=100.0
2.5
t=200.0
2.0
2.0
2.0
U(x,t)
1.5
U(x,t)
1.5
U(x,t)
1.5
1.0
1.0
1.0
0.5
0.5
0.5
0.0
0 π/2 π 3π/2 2π
x
3.0
3.0
0.0
0 π/2 π 3π/2 2π
x
Wave propagation with spectral method:
0.0
0 π/2 π 3π/2 2π
x
3.0
N=10
N=10
N=10
2.5
t=0.0
2.5
t=100.0
2.5
t=200.0
2.0
2.0
2.0
U(x,t)
1.5
U(x,t)
1.5
U(x,t)
1.5
1.0
1.0
1.0
0.5
0.5
0.5
0.0
0 π/2 π 3π/2 2π
x
0.0
0 π/2 π 3π/2 2π
x
Figures from Hesthaven, Gottlieb, & Gottlieb (2007).
0.0
0 π/2 π 3π/2 2π
x
Lee Lindblom (Caltech) Binary Black Holes UW Milwaukee 10/14/2011 19 / 32