@article{brown_lowe_2006, title={Modifying the Einstein equations off the constraint hypersurface}, volume={74}, ISSN={["2470-0029"]}, url={http://inspirehep.net/record/718410}, DOI={10.1103/physrevd.74.104023}, abstractNote={A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.}, number={10}, journal={PHYSICAL REVIEW D}, author={Brown, J. David and Lowe, Lisa L.}, year={2006}, month={Nov} }
 @article{brown_lowe_2005, title={Multigrid elliptic equation solver with adaptive mesh refinement}, volume={209}, ISSN={["1090-2716"]}, url={http://inspirehep.net/record/665142}, DOI={10.1016/j.jcp.2005.03.026}, abstractNote={In this paper, we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by adaptive mesh refinement.}, number={2}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Brown, JD and Lowe, LL}, year={2005}, month={Nov}, pages={582–598} }
 @article{brown_lowe_2004, title={Distorted black hole initial data using the puncture method}, volume={70}, ISSN={["1550-2368"]}, url={http://inspirehep.net/record/657537}, DOI={10.1103/physrevd.70.124014}, abstractNote={We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R{sup 3} for the nonsingular part of the metric conformal factor. With this approach we can generate isometric and nonisometric black hole data. For the isometric case, our data are directly comparable to those obtained by Bernstein et al., who impose isometry boundary conditions at the black hole throat. Our numerical simulations are performed using a parallel multigrid elliptic equation solver with adaptive mesh refinement. Mesh refinement allows us to use high resolution around the black hole while keeping the grid boundaries far away in the asymptotic region.}, number={12}, journal={PHYSICAL REVIEW D}, author={Brown, JD and Lowe, LL}, year={2004}, month={Dec} }