SpECTRE
v2024.09.29

This page highlights some visualizations of SpECTRE simulations.
SpECTRE can simulate black holes that orbit each other and eventually merge, emitting gravitational waves. SpECTRE uses the Generalized Harmonic formulation of Einstein's equations of general relativity to solve this problem. Since we expect the solution of Einstein's equations to be smooth for the BBH problem, we represent our solution using the Discontinuous Galerkin (DG) method because of its ability to represent smooth functions to high accuracy. Also, DG allows SpECTRE to parallelize the BBH problem.
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SpECTRE can generate initial data to start simulations of merging black holes. This problem involves solving the elliptic constraint sector of the Einstein equations for a slice of spacetime that contains two black holes with the requested parameters. SpECTRE uses the XCTS formulation with a nonconformallyflat background defined by the superposed KerrSchild formalism to reach high spins. Black holes are represented by excisions and boundary conditions.
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SpECTRE implements a novel Cauchycharacteristic evolution (CCE) system for extracting gravitational waveforms from our simulations. It evolves the Einstein equations on null slices to infinity, which is more accurate than extrapolation and allows us to extract the gravitational memory effect. The CCE waveform extraction is publicly available as a standalone module.
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SpECTRE can simulate merging neutron stars and other generalrelativistic magnetohydrodynamic (GRMHD) problems with dynamic gravity. Our DGFD hybrid scheme accelerates smooth regions of the grid with highorder spectral methods (see DGFD hybrid method).
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Our computational domains in SpECTRE are designed to adapt to the geometry of the problems we want to solve. They can be curved, e.g. to wrap around excision regions in binary black hole problems (see Binary black hole mergers) or to resolve the wavezone in binary neutron star merger. They can also rotate and deform in time using control systems, which reactively adjust coordinate maps to track the position and shape of the black hole excisions or neutron stars.
Our discontinuous Galerkin methods allow two types of mesh refinement: splitting elements in half along any dimension (hrefinement) or increasing their polynomial expansion order (prefinement). The former allows us to distribute computational cost to supercomputers, while the latter allows us to use these resources efficiently by decreasing the numerical error exponentially with the number of grid points where the solution is smooth. Our adaptive mesh refinement technology decides which type of refinement to apply in each region of the domain.
Our hydrodynamical simulations use a discontinuous Galerkinfinite difference (DGFD) hybrid method: smooth regions of the simulation are evolved with an efficient DG scheme and nonsmooth regions fall back to a robust FD method. Shocks and discontinuities on the grid are tracked with a troubledcell indicator (TCI) to switch between DG and FD. This approach accelerates our simulations by reducing the computational resources spent on smooth regions of the grid, e.g. when evolving inspiral binary neutron stars and their gravitational radiation.
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SpECTRE can generate initial data for binary black holes in scalar GaussBonnet gravity, evolve the modified Einstein equations, and extract the gravitational and scalar radiation.
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We have applied the SpECTRE technology to an interdisciplinary problem, simulating the Brownian thermal noise in the mirrors of interferometric gravitationalwave detectors at unprecedented accuracy. It uses the SpECTRE elliptic solver [197] to solve an elasticity problem, which connects to the thermal noise problem through the fluctuation dissipation theorem.
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