Solving Einstein's Equations on Supercomputers

Proceedings. Frontiers '99. Seventh Symposium on the Frontiers of Massively Parallel Computation, 1999

We are developing a system for collaborative research and development for a distributed group of researchers at different institutions around the world. In a new paradigm for collaborative computational science, the computer code and supporting infrastructure itself becomes the collaborating instrument, just as an accelerator becomes the collaborating tool for large numbers of distributed researchers in particle physics. The design of this "Collaboratory" allows many users, with very different areas of expertise, to work coherently together, on distributed computers around the world. Different supercomputers may be used separately, or for problems exceeding the capacity of any single system, multiple supercomputers may be networked together through high speed gigabit networks. Central to this Collaboratory is a new type of community simulation code, called "Cactus". The scientific driving force behind this project is the simulation of Einstein's equations for studying black holes, gravitational waves, and neutron stars, which has brought together researchers in very different fields from many groups around the world to make advances in the study of relativity and astrophysics. But the system is also being developed to provide scientists and engineers, without expert knowledge of parallel or distributed computing, mesh refinement, and so on, with a simple framework for solving any system of partial differential equations on many parallel computer systems, from traditional supercomputers to networks of workstations.

Journal of Computational and Applied Mathematics, 1999

Classical and Quantum Gravity, 2012

We describe the Einstein Toolkit, a community-driven, freely accessible computational infrastructure intended for use in numerical relativity, relativistic astrophysics, and other applications. The Toolkit, developed by a collaboration involving researchers from multiple institutions around the world, combines a core set of components needed to simulate astrophysical objects such as black holes, compact objects, and collapsing stars, as well as a full suite of analysis tools. The Einstein Toolkit is currently based on the Cactus Framework for high-performance computing and the Carpet adaptive mesh refinement driver. It implements spacetime evolution via the BSSN evolution system and general-relativistic hydrodynamics in a finite-volume discretization. The toolkit is under continuous development and contains many new code components that have been publicly released for the first time and are described in this article. We discuss the motivation behind the release of the toolkit, the philosophy underlying its development, and the goals of the project. A summary of the implemented numerical techniques is included, as are results of numerical test covering a variety of sample astrophysical problems.

1999

We are developing a system for collaborative research and development for a distributed group of researchers at different institutions around the world. In a new paradigm for collaborative computational science, the computer code and supporting infrastructure itself becomes the collaborating instrument, just as an accelerator becomes the collaborating tool for large numbers of distributed researchers in particle physics. The design of this “collaboratory” allows many users, with very different areas of expertise, to work coherently together, on distributed computers around the world. Different supercomputers may be used separately, or for problems exceeding the capacity of any single system, multiple supercomputers may be networked together through high speed gigabit networks. Central to this collaboratory is a new type of community simulation code, called “Cactus”. The scientific driving force behind this project is the simulation of Einstein's equations for studying black holes, gravitational waves, and neutron stars, which has brought together researchers in very different fields from many groups around the world to make advances in the study of relativity and astrophysics. But the system is also being developed to provide scientists and engineers, without expert knowledge of parallel or distributed computing, mesh refinement, and so on, with a simple framework for solving any system of partial differential equations on many parallel computer systems, from traditional supercomputers to networks of workstations

2016

In this paper, we’ll attempt to provide a “vertical slice” of general relativity providing the reader with the bare minimum needed to get from classical mechanics to a fully-featured real-time black hole renderer. We’ll assume the reader has some semi-intuitive familiarity with some general aspects of relativity for instance, that gravity curves the path of light rays, or that unusual things happen around black hole singularities. While we won’t shy away from going into the underlying mathematics that allows the computation of relativistic phenomena, we’ll also attempt to motivate the mathematics with physical or theoretical examples as much as possible. The final raytracer implementation is largely based on James, Tunzelmann, Franklin, and Thorne’s description of the Double Negative Gravitational Renderer built to deliver 12K imagery for Christopher Nolan’s Interstellar (James et al., 2015). Our final source is about 1/470th as long as that of DNGR; as such, there are many real-wor...

2007

This paper presents a review of the use of Computer Algebra Systems in General Relativity research and teaching. On one hand, the impact of using Computer Algebra Systems in General Relativity research is illustrated by pointing out some important achievements in the field. In particular, by using Computer Algebra Systems, the present author has been able to obtain results that would have been almost impossible otherwise. On the other hand, Computer Algebra Systems can be a very helpful tool in teaching and learning GR. Some reports on using Computer Algebra Systems in teaching General Relativity are outlined.

International Journal of Modern Physics C, 2002

The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application ("thorn") for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these wellknown examples, focusing mainly on the stability and convergence of the code. * Permanent address : The

We study three computer algebra systems, namely SageMath (with SageManfolds package), Maxima (with ctensor package) and Python language (with GraviPy module), which allow tensor manipulation for general relativity calculations. We present simple examples and give a benchmark of these systems. After the general analysis, we focus on the SageMath+SageManifolds system to analyze and visualize the solutions of the massless Klein–Gordon equation and geodesic motion with Hamilton–Jacobi formalism.

Classical and Quantum Gravity, 2002

We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed to run over the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII used to perform on line coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows for systematic internal self-checking and a minimization of the required internal records. This new database is now on line at http://grdb.org.

International Journal of …, 2001

The Cactus software package is suitable for a class of scientific applications that are tightly coupled, have regular space decompositions, and involve huge memory and processor time requirements. Cactus has proved to be a valuable tool for astrophysicists, who first initiated its development. However, today's fastest supercomputers are not powerful enough to perform realistic large-scale astrophysics simulations with Cactus. Instead, astrophysicists must turn to innovative resource environments-in particular, computational grids-to satisfy this need for computational power. This paper addresses issues related to the execution of applications such as Cactus in grid environments. The authors focus on two types of grids: a set of geographically distributed supercomputers and a collection of one million Internet-connected workstations. The authors study the application performance on traditional systems, validate the theoretical results against experimental data, and predict performance in the two new environments.