TY - JOUR
T1 - Initial conditions for numerical relativity
T2 - Introduction to numerical methods for solving elliptic pdes
AU - Okawa, Hirotada
N1 - Funding Information:
The author is thankful to Ana Sousa who helps to improve English on this notes, Sérgio Almeida who maintains the cluster “Baltasar-Sete-Sóis” and Takashi Hira-matsu who maintains the “venus” cluster. Numerical computations in this work were carried out on the cluster of “Baltasar-Sete-Sóis” at Instituto Superior Técnico in Lisbon which is supported by the DyBHo-256667 ERC Starting Grant and on the “venus” cluster at the Yukawa Institute Computer Facility in Kyoto University. This work was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation.
PY - 2013/9/20
Y1 - 2013/9/20
N2 - Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to evolve such systems, a proper understanding of the methods involved is quite important. Here, we focus on the numerical solution of elliptic partial differential equations. Such equations arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes. Because such elliptic equations play an important role in many branches of physics, we give an overview of the topic, and show how to numerically solve them with simple examples and sample codes written in C++ and Fortran90 for beginners in numerical relativity or other fields requiring numerical expertise.
AB - Numerical relativity became a powerful tool to investigate the dynamics of binary problems with black holes or neutron stars as well as the very structure of General Relativity. Although public numerical relativity codes are available to evolve such systems, a proper understanding of the methods involved is quite important. Here, we focus on the numerical solution of elliptic partial differential equations. Such equations arise when preparing initial data for numerical relativity, but also for monitoring the evolution of black holes. Because such elliptic equations play an important role in many branches of physics, we give an overview of the topic, and show how to numerically solve them with simple examples and sample codes written in C++ and Fortran90 for beginners in numerical relativity or other fields requiring numerical expertise.
KW - Black hole
KW - Numerical method
KW - Numerical relativity
UR - http://www.scopus.com/inward/record.url?scp=84884840673&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84884840673&partnerID=8YFLogxK
U2 - 10.1142/S0217751X13400162
DO - 10.1142/S0217751X13400162
M3 - Article
AN - SCOPUS:84884840673
SN - 0217-751X
VL - 28
JO - International Journal of Modern Physics A
JF - International Journal of Modern Physics A
IS - 22-23
M1 - 1340016
ER -