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Abstract Neutron stars have solid crusts threaded by strong magnetic fields. Perturbations in the crust can excite nonradial oscillations, which can in turn launch Alfvén waves into the magnetosphere. In the case of a compact binary close to merger involving at least one neutron star, this can happen through tidal interactions causing resonant excitations that shatter the neutron star crust. We present the first numerical study that elucidates the dynamics of Alfvén waves launched in a compact binary magnetosphere. We seed a magnetic field perturbation on the neutron star crust, which we then evolve in fully general-relativistic force-free electrodynamics using a GPU-based implementation. We show that Alfvén waves steepen nonlinearly before reaching the orbital light cylinder, form flares, and dissipate energy in a transient current sheet. Our results predict radio and X-ray precursor emission from this process. 

SpECTRE is an open-source code for multi-scale, multi-physics problems in astrophysics and gravitational physics. In the future, we hope that it can be applied to problems across discipline boundaries in fluid dynamics, geoscience, plasma physics, nuclear physics, and engineering. It runs at petascale and is designed for future exascale computers. SpECTRE is being developed in support of our collaborative Simulating eXtreme Spacetimes (SXS) research program into the multi-messenger astrophysics of neutron star mergers, core-collapse supernovae, and gamma-ray bursts. 

We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is achieved by monitoring the relative power in the highest mode of the reconstructed polynomial and reducing the order when the polynomial series no longer converges. Our approach is similar to the multidimensional optimal order detection strategy, but differs in several ways. The approach isa prioriand so does not require retaking a time step. It can also readily be combined with positivity-preserving flux limiters that have gained significant traction in computational astrophysics and numerical relativity. This combination ultimately guarantees a physical solution both during reconstruction and time stepping. We demonstrate the capabilities of the method using a standard suite of very challenging 1d, 2d, and 3d general relativistic magnetohydrodynamics test problems. 

Abstract We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.