@article {Darmofal_1999_RobustMultigrid_LPC_SC,
	title = {A Robust Multigrid Algorithm for the Euler Equations with Local Preconditioning and Semi-coarsening},
	journal = {Journal of Computational Physics},
	volume = {151},
	number = {2},
	year = {1999},
	pages = {728 - 756},
	abstract = {A semi-coarsened multigrid algorithm with a point block Jacobi, multi-stage smoother for second-order upwind discretizations of the two-dimensional Euler equations which produces convergence rates independent of grid size for moderate subsonic Mach numbers is presented. By modification of this base algorithm to include local preconditioning for low Mach number flows, the convergence becomes largely independent of grid size and Mach number over a range of flow conditions from nearly incompressible to transonic flows, including internal and external flows. A local limiting technique is introduced to increase the robustness of preconditioning in the presence of stagnation points. Computational timings are made showing that the semi-coarsening algorithm requiresO(N) time to lower the fine grid residual six orders of magnitude, whereNis the number of cells. By comparison, the same algorithm applied to a full-coarsening approach requiresO(N3/2) time, and, in nearly all cases, the semi-coarsening algorithm is faster than full coarsening with the computational savings being greatest on the finest grids.},
	issn = {0021-9991},
	doi = {10.1006/jcph.1999.6216},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999199962162},
	author = {Darmofal, D L and Siu, K}
}
@mastersthesis {Siu_1998_SM,
	title = {A Robust, Locally Preconditioned Multigrid Algorithm for the Euler Equations},
	year = {1998},
	school = {Texas A\&M University},
	type = {masters},
	address = {Department of Aerospace Engineering},
	author = {Siu, K}
}
