Fundamental Issues of Numerical Relativity
Assumptions /
Restrictions
(for this talk)
Nature of Relativistic Gravitation
Black Holes and Physical Singularities
Singularity Avoidance: Black Hole Excision
Core Mathematical
Problem
“They’re just a set of PDEs, Larry”
A Principle One Can Take to
the Bank
(Brandt’s “Golden Rule”)
Flip Side of The Golden
Rule
(The No Free Lunch Principle)
Building “Good” Coordinate Systems
Kreiss-Oliger Dissipation: Example
Kreiss-Oliger Dissipation: Example
Effect of
Dissipation
65 x 129 Grid
(Axisymmetric collapse of scalar field)
Effect of
Dissipation
65 x 129 Grid
Effect of
Dissipation
65 x 129 Grid
Effect of
Dissipation
129 x 257 grid
Effect of
Dissipation
129 x 257 grid
Effect of
Dissipation
129 x 257 grid
Effect of
Dissipation
127 x 259 grid
Adaptive Mesh
Refinement
(near-critical axisymmetric collapse of scalar field)
Adaptive Mesh
Refinement
(near-critical axisymmetric collapse of scalar field)