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This paper synthesizes formally orthogonal polynomials, Gaussian quadrature in the complex plane and the bi-conjugate gradient method together with an application. Classical Gaussian quadrature approximates an integral over (a region of) the real line. We present an extension of Gaussian quadrature over an arc in the complex plane, which we call complex(More)
Two natural and efficient stopping criteria are derived for conjugate gradient (CG) methods, based on iteration parameters. The derivation makes use of the inner product matrix B defining the CG method. In particular, the relationship between the eigenvalues and B-norm of a matrix is investigated, and it is shown that the ratio of largest to smallest(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)
Flux-limited diffusion has become a popular method for treating radiation transport in multidimensional as-trophysical simulation codes with multi-group flux-limited diffusion (MGFLD) undergoing increasing use in a number of applications. The most computationally demanding aspect of this technique is the solution of the large linear systems that arise from(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)
We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a selection of distorted, moving and spinning single black holes, with evolution times up to 60, 000M. Accurate numerical(More)
I asked Johnson if solving linear equations was a big part of the computational load at the laboratory. He said it must be about seventy-five percent of the machine time, but that his work to try to improve linear equation routines was mostly ineffectual. "You would go into the code and think you had it running faster, then they'd change the geometry or(More)