NRPy+/SENR is a numerical relativity code package aimed at solving the full set of Einstein's equations of general relativity to model compact objects at about 1/100 the cost in memory of more traditional, AMR-based numerical relativity codes, unlocking the desktop computer as a core tool for gravitational wave astrophysics.

NRPy+/SENR gains this enormous efficiency boost via a new, dynamic reference metric formalism. The code is designed to be open-development, human-readable, compact, OpenMP parallelized, and easily-extensible.

NRPy+ ("Python-based Code generation for Numerical Relativity and Beyond") is a new open-source code generation package, in which users may input complex tensorial expressions in Einstein-like notation, and the Python-based code will generate highly-optimized C code. NRPy+ uses SymPy as its computer algebra system backend.

SENR ("the Simple, Efficient Numerical Relativity code") is a fully-functional, OpenMP parallelized numerical relativity code in C that simply incorporates the C code generated by NRPy+ where needed. Its uncluttered appearance and small number of lines of code make the algorithmic underpinnings of a numerical relativity code transparent to the user.

We are currently working to extend existing reference metric formalisms that produce static coordinate grids, to generate dynamic, bispherical-like coordinate grids. Such grids will be useful for modeling compact binaries in a co-rotating frame.

New! (Updated Aug 2018) Interactive NRPy+ Tutorial. (Jupyter notebooks hosted by

New! (June 2018) SENR can do black hole binary mergers in a co-rotating frame!

Introductory presentation on NRPy+/SENR.

Current Status

An at-a-glance summary of the latest results of our ongoing projects. To see more updates, click the figure below or the navigation bar above.

Dec 22, 2017: Released first paper on NRPy+/SENR

Recent results (prior to the black hole binary work) are summarized in our first paper.

Key Result from First Paper: Black Hole Spectroscopy

We performed a black hole head-on collision simulation with SENR in sinh-spherical coordinates, and compared the resulting waveform (as measured by the absolute value of the real part of the Weyl scalar \Psi_4; the vertical scale is arbitrary) from our calculation with the exponentially decaying waveform predicted by black hole perturbation theory.

Notice that we find excellent phase and amplitude agreement to nearly 7 decades in amplitude. The same calculation performed on a Cartesian AMR grid at high resolution results in disagreement after only about 3 or 4 decades, indicating the importance of using spherical-like coordinates in the gravitational wavezone.

Click the figure to learn more about SENR!

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Zachariah B. Etienne is an assistant professor of mathematics at West Virginia University.

Ian Ruchlin is a post doctoral research associate in the mathematics department at West Virginia University.

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