Mark A. Scheel

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A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially suppresses all small short-wavelength constraint violations. Physical and constraint-preserving boundary conditions are(More)
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one-to three-dimensional problems. It has three distinct features. First, the combined problem of solving the PDE, satisfying the boundary conditions, and matching between(More)
Techniques are developed for projecting the solutions of symmetric hyperbolic evolution systems onto the constraint submanifold (the constraint-satisfying subset of the dynamical field space). These optimal projections map a field configuration to the " nearest " configuration in the constraint submanifold, where distances between configurations are(More)
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the(More)
We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present(More)
We calibrate the effective-one-body (EOB) model to an accurate numerical simulation of an equal-mass, nonspinning binary black-hole coalescence produced by the Caltech-Cornell Collaboration. Aligning the EOB and numerical waveforms at low frequency over a time interval of $1000M, and taking into account the uncertainties in the numerical simulation, we(More)
Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a 'reference' numerical solution obtained by placing the outer boundary at a very large(More)
Binary black-hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three-dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational(More)
When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E(jk) that describes tidal gravity and a "magnetic" part B(jk) that describes differential dragging of inertial frames. We introduce tools for visualizing B(jk) (frame-drag vortex lines, their vorticity, and vortexes) and E(jk) (tidal(More)
Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black(More)