A new family of preconditioners for conjugate gradient-like iterative methods applied to large sparse linear least squares problems, min k Ax ? b k 2 , is proposed. The family is based on incomplete Gram-Schmidt (IGS) factorizations of A. Particular attention has been given to the following members of the family: Incomplete Classical Gram-Schmidt (ICGS),… (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)
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)
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)
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)
Refereed Journal Publications 1. " Variational iterative methods for nonsymmetric systems of linear equations, " with 2. " Preconditioning by fast direct methods for non-self-adjoint nonseparable elliptic equations, " with M. 3. " A hybrid Chebyshev Krylov-subspace algorithm for solving nonsymmetric systems of linear equations, " with Y.