Lee Lindblom

A New generalized harmonic evolution system

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 derived for this system, and numerical tests that demonstrate the effectiveness of the constraint suppression properties and the constraint-preserving boundary conditions are presented.

Solving Einstein's equations with dual coordinate frames

A method is introduced for solving Einsteins equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the way fields are projected onto an orthonormal tetrad basis. These field components are then determined as functions of a second independent coordinate system. The transformation to the second coordinate system can be thought of as a mapping from the original inertial coordinate system to the computational domain. This dual-coordinate method is used to perform stable numerical evolutions of a black-hole spacetime using the generalized harmonic form of Einsteins equations in coordinates that rotate with respect to the inertial frame at infinity; such evolutions are found to be generically unstable using a single rotating-coordinate frame. The dual-coordinate method is also used here to evolve binary black-hole spacetimes for several orbits. The great flexibility of this method allows comoving coordinates to be adjusted with a feedback control system that keeps the excision boundaries of the holes within their respective apparent horizons.

Simulations of Binary Black Hole Mergers Using Spectral Methods

Several improvements in numerical methods and gauge choice are presented that make it possible now to perform simulations of the merger and ringdown phases of ``generic binary black hole evolutions using the pseudospectral evolution code SpEC. These improvements include the use of a new damped-wave gauge condition, a new grid structure with appropriate filtering that improves stability, and better adaptivity in conforming the grid structures to the shapes and sizes of the black holes. Simulations illustrating the success of these new methods are presented for a variety of binary black hole systems. These include fairly generic systems with unequal masses (up to

Optimal constraint projection for hyperbolic evolution systems

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Model waveform accuracy standards for gravitational wave data analysis

mass ratios), and spins (with magnitudes up to

Boundary conditions for the Einstein evolution system

0.4{M}^{2}

Reducing orbital eccentricity in binary black hole simulations

) pointing in various directions.

Testing outer boundary treatments for the Einstein equations

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 measured with the natural metric on the space of dynamical fields. The construction and use of these projections are illustrated for a new representation of the scalar field equation that exhibits both bulk and boundary generated constraint violations. Numerical simulations on a black hole background show that bulk constraint violations cannot be controlled by constraint-preserving boundary conditions alone, but are effectively controlled by constraint projection. Simulations also show that constraint violations entering through boundaries cannot be controlled by constraint projection alone, but are controlled by constraint-preserving boundary conditions. Numerical solutions to the pathological scalar field system are shown to converge to solutions of a standard representation of the scalar field equation when constraint projection and constraint-preserving boundary conditions are used together.

Controlling the growth of constraints in hyperbolic evolution systems

Model waveforms are used in gravitational wave data analysis to detect and then to measure the properties of a source by matching the model waveforms to the signal from a detector. This paper derives accuracy standards for model waveforms which are sufficient to ensure that these data analysis applications are capable of extracting the full scientific content of the data, but without demanding excessive accuracy that would place undue burdens on the model waveform simulation community. These accuracy standards are intended primarily for broadband model waveforms produced by numerical simulations, but the standards are quite general and apply equally to such waveforms produced by analytical or hybrid analytical-numerical methods.

Models of rapidly rotating neutron stars: remnants of accretion-induced collapse

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike boundaries, allow the simulation of isolated systems by preventing physical gravitational waves from entering the computational domain, and are designed to be compatible with the fixed-gauge evolutions used here. These new boundary conditions are shown to be effective in limiting the growth of constraints in 3D nonlinear numerical evolutions of dynamical black-hole spacetimes.