TY - JOUR
T1 - Three-dimensional initial data for the collision of two black holes
AU - Cook, Gregory B.
AU - Choptuik, Matthew W.
AU - Dubal, Mark R.
AU - Klasky, Scott
AU - Matzner, Richard A.
AU - Oliveira, Samuel R.
PY - 1993
Y1 - 1993
N2 - We describe three numerical approaches to the construction of three-dimensional initial data for the collision of two black holes. The first of our approaches involves finite differencing the 3 + 1 Hamiltonian constraint equation on a ade coordinate grid. The difference equations are then solved via the multigrid algorithm. The second approach also uses finite-difference techniques, but this time on a regular Cartesian coordinate grid. A Cartesian grid has the advantage of having no coordinate singularities. However, constant coordinate lines are not coincident with the throats of the black holes and, therefore, special treatment of the difference equations at these boundaries is required. The resulting equations are solved using a variant of line-successive overrelaxation. The third and final approach we use is a global, spectral-like method known as the multiquadric approximation scheme. In this case functions are approximated by a finite sum of weighted quadric basis functions which are continuously differentiable. We discuss particular advantages and disadvantages of each method and compare their performances on a set of test problems.
AB - We describe three numerical approaches to the construction of three-dimensional initial data for the collision of two black holes. The first of our approaches involves finite differencing the 3 + 1 Hamiltonian constraint equation on a ade coordinate grid. The difference equations are then solved via the multigrid algorithm. The second approach also uses finite-difference techniques, but this time on a regular Cartesian coordinate grid. A Cartesian grid has the advantage of having no coordinate singularities. However, constant coordinate lines are not coincident with the throats of the black holes and, therefore, special treatment of the difference equations at these boundaries is required. The resulting equations are solved using a variant of line-successive overrelaxation. The third and final approach we use is a global, spectral-like method known as the multiquadric approximation scheme. In this case functions are approximated by a finite sum of weighted quadric basis functions which are continuously differentiable. We discuss particular advantages and disadvantages of each method and compare their performances on a set of test problems.
UR - http://www.scopus.com/inward/record.url?scp=33845636781&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.47.1471
DO - 10.1103/PhysRevD.47.1471
M3 - Article
AN - SCOPUS:33845636781
SN - 0556-2821
VL - 47
SP - 1471
EP - 1490
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 4
ER -