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We introduce NRPyElliptic, an elliptic solver for numerical relativity (NR) built within the NRPy+ framework. As its first application, NRPyElliptic sets up conformally flat, binary black hole (BBH) puncture initial data (ID) on a single numerical domain, similar to the widely used TwoPunctures code. Unlike TwoPunctures, NRPyElliptic employs a hyperbolic relaxation scheme, whereby arbitrary elliptic PDEs are trivially transformed into a hyperbolic system of PDEs. As consumers of NR ID generally already possess expertise in solving hyperbolic PDEs, they will generally find NRPyElliptic easier to tweak and extend than other NR elliptic solvers. When evolved forward in (pseudo)time, the hyperbolic system exponentially reaches a steady state that solves the elliptic PDEs. Notably NRPyElliptic accelerates the relaxation waves, which makes it many orders of magnitude faster than the usual constant-wavespeed approach. While it is still ∼12x slower than TwoPunctures at setting up full-3D BBH ID, NRPyElliptic requires only ≈0.3% of the runtime for a full BBH simulation in the Einstein Toolkit. Future work will focus on improving performance and generating other types of ID, such as binary neutron star.
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RoeNet: Predicting discontinuity of hyperbolic systems from continuous data
Abstract Predicting future discontinuous phenomena that are unobservable from training data sets has long been a challenging problem in scientific machine learning. We introduce a novel paradigm to predict the emergence and evolution of various discontinuities of hyperbolic partial differential equations (PDEs) based on given training data over a short window with limited discontinuity information. Our method is inspired by the classical Roe solver [P. L. Roe, J Comput Phys., vol. 43, 1981], a basic tool for simulating various hyperbolic PDEs in computational physics. By carefully designing the computing primitives, the data flow, and the novel pseudoinverse processing module, we enable our data‐driven predictor to satisfy all the essential mathematical criteria of a Roe solver and hence deliver accurate predictions of hyperbolic PDEs. We demonstrate through various examples that our data‐driven Roe predictor outperforms original human‐designed Roe solver and deep neural networks with weak priors in terms of accuracy and robustness.
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- Award ID(s):
- 1919647
- PAR ID:
- 10479542
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Engineering
- ISSN:
- 0029-5981
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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