Multi-physics coupling of Einstein and hydrodynamics evolution: a case study of the Einstein toolkit

Cactus is a software framework for high-performance computing which sees widespread use in the numerical relativity community and other fields. The Einstein Toolkit is a set of Cactus components providing infrastructure and basic functionality for, and enabling interoperability between, different general relativistic applications codes. In particular, the Einstein Toolkit provides an efficient coupling mechanism between spacetime (Einstein) and relativistic hydrodynamics (Euler) evolution components. This provides coupling in the volume, where both Einstein and Euler equations are integrated simultaneously everywhere in the domain on co-located grids. Several independent but interoperable Einstein and hydrodynamics codes have been built on this toolkit by different research groups over the past decade. Below we introduce the Einstein Toolkit and describe the coupling mechanism. We discuss certain trade-offs regarding simplicity, continuity with historical coincidence, performance, and memory consumption. We briefly mention the process which lead to the current design and outline future plans. Where appropriate, we draw parallels between solving the Einstein and the Maxwell (electrodynamics) equations, in effect outlining a possible design of an equivalent toolkit for coupling the Maxwell and the hydrodynamics equations.

[1]  Erik Schnetter,et al.  Gauge fixing for the simulation of black hole spacetimes , 2003 .

[2]  W. Kastaun.  Developing a code for general relativistic hydrodynamics with application to neutron star oscillations , 2006 .

[3]  William H. Press,et al.  Numerical recipes , 1990 .

[4]  E. Seidel,et al.  Towards a stable numerical evolution of strongly gravitating systems in general relativity: The conformal treatments , 2000, gr-qc/0003071.

[5]  M. Campanelli,et al.  Accurate black hole evolutions by fourth-order numerical relativity , 2005 .

[6]  John Shalf,et al.  The Cactus Framework and Toolkit: Design and Applications , 2002, VECPAR.

[7]  Binary black-hole evolutions of excision and puncture data , 2006, gr-qc/0606079.

[8]  Samuel Williams,et al.  Lattice Boltzmann simulation optimization on leading multicore platforms , 2008, 2008 IEEE International Symposium on Parallel and Distributed Processing.

[9]  Gabrielle Allen,et al.  A case study for petascale applications in astrophysics: simulating gamma-ray bursts , 2008, Mardi Gras Conference.

[10]  R. Arnowitt,et al.  Republication of: The dynamics of general relativity , 2004 .

[11]  Christiane Lechner,et al.  Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations , 2006, Comput. Phys. Commun..

[12]  Lawrence E. Kidder,et al.  Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations , 2001, gr-qc/0105031.

[13]  L. Rezzolla,et al.  An explicit harmonic code for black-hole evolution using excision , 2006, gr-qc/0612150.

[14]  Scott H. Hawley,et al.  Evolutions in 3D numerical relativity using fixed mesh refinement , 2003, gr-qc/0310042.

[15]  Department of Physics,et al.  WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics , 2007, gr-qc/0701109.

[16]  Well-Posed Initial-Boundary Evolution in General Relativity , 2002, gr-qc/0205044.

[17]  Cauchy boundaries in linearized gravitational theory , 1999, gr-qc/9912030.

[18]  Z. Etienne,et al.  Relativistic hydrodynamics in the presence of puncture black holes , 2007, 0708.2436.

[19]  Burkhard Zink,et al.  A general relativistic evolution code on CUDA architectures , 2008 .

[20]  Christiane Lechner,et al.  From Tensor Equations to Numerical Code - Computer Algebra Tools for Numerical Relativity , 2004, ArXiv.

[21]  Jacques E. Romain,et al.  Gravitation: An Introduction to Current Research , 1963 .

[22]  John Shalf,et al.  Cactus Framework: Black Holes to Gamma Ray Bursts , 2007, ArXiv.

[23]  C. Ott,et al.  3D collapse of rotating stellar iron cores in general relativity including deleptonization and a nuclear equation of state. , 2006, Physical review letters.

[24]  Matched filtering of numerical relativity templates of spinning binary black holes , 2007, 0705.3829.

[25]  E. Schnetter,et al.  Black hole head-on collisions and gravitational waves with fixed mesh-refinement and dynamic singularity excision , 2005 .

[26]  E. Seidel,et al.  Gauge conditions for long-term numerical black hole evolutions without excision , 2002, gr-qc/0206072.

[27]  E. Schnetter,et al.  A multi-block infrastructure for three-dimensional time-dependent numerical relativity , 2006, gr-qc/0602104.

[28]  L. Baiotti,et al.  A new three-dimensional general-relativistic hydrodynamics code , 2010, 1004.3849.

[29]  Lifan Wang,et al.  The supernova-gamma-ray burst connection , 1998, astro-ph/9806212.

[30]  Leonid Oliker,et al.  Scientific Application Performance on Candidate PetaScale Platforms , 2007, 2007 IEEE International Parallel and Distributed Processing Symposium.

[31]  Erik Schnetter,et al.  Multipatch methods in general relativistic astrophysics: Hydrodynamical flows on fixed backgrounds , 2007, 0712.0353.

[32]  S. Husa,et al.  Kranc : a Mathematica application to generate numerical codes for tensorial evolution equations , 2004 .

[33]  L. Baiotti,et al.  Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole , 2004, gr-qc/0403029.