In preparation:
NonHermitian coarsening strategies for algebraic multigrid, S. MacLachlan.
Implied volatility and the riskfree rate of return in options markets, M. Bianconi, S. MacLachlan, and M. Sammon, January 2014.
Journal Articles:
An energyminimization finiteelement approach for the FrankOseen model of nematic liquid crystals, J. H. Adler, T. J. Atherton, D. B. Emerson, and S. P. MacLachlan, submitted, 2014.
Mathematical and computational models of incompressible materials subject to shear, J.H. Adler, L. Dorfmann, D. Han, S. MacLachlan, and C. Paetsch, revised, 2014.
A generalized predictive analysis tool for multigrid methods, S. Friedhoff and S. MacLachlan, submitted, 2013.
Parallel time integration with multigrid, R.D. Falgout, S. Friedhoff, Tz.V. Kolev, S.P. MacLachlan, and J.B. Schroder, submitted, 2013.
Theoretical bounds for algebraic multigrid performance: review and analysis,
S. MacLachlan and L. Olson, Numer. Linear Alg. Appl., 21(2):194220, 2014.
Local Fourier analysis of
spacetime relaxation and multigrid schemes, S. Friedhoff,
S. MacLachlan and C. Börgers,
SIAM J. Sci. Comput., 35:S250276, 2013.
Robust solution of singularly perturbed
problems using multigrid methods, S. MacLachlan and N. Madden,
SIAM J. Sci. Comput., 35:A2225A2254, 2013.
Comparison of the deflated
preconditioned conjugate gradient method and algebraic multigrid for
composite materials, T.B. Jönsthövel, M.B. van
Gijzen, S. MacLachlan, C. Vuik, and A. Scarpas, Computational
Mechanics, 50:321333, 2012.
Modification and compensation strategies for thresholdbased
incomplete factorizations,
S. MacLachlan, D. OseiKuffuor, and Y. Saad, SIAM
J. Sci. Comput., 34:A48A75, 2012.
Robust and Adaptive Multigrid Methods:
comparing structured and algebraic approaches,
S.P. MacLachlan, J.D. Moulton, and T.P. Chartier, Numerical
Linear Algebra with Applications, 19:389413, 2012.
Iterative parameter choice and
algebraic multigrid for anisotropic diffusion denoising,
D. Chen, S. MacLachlan, and M. Kilmer, SIAM J. Sci. Comp., 33:29722994, 2011.
Local Fourier analysis for
multigrid with overlapping smoothers applied to systems of
PDEs, S.P. MacLachlan and C.W. Oosterlee, Numerical
Linear Algebra with Applications, 18:751774, 2011.
A fast method for the solution of
the Helmholtz equation, E. Haber and S. MacLachlan,
J. Comp. Phys., 230(12):44034418,
2011.
On iterative methods for the incompressible Stokes problem,
M. ur Rehman, T. Geenen, C. Vuik, G. Segal, and
S.P. MacLachlan, International Journal for Numerical Methods in
Fluids, 65(10):11801200, 2011.
A geometric multigrid method based on
Lshaped coarsening for PDEs on stretched grids, H. bin Zubair,
S.P. MacLachlan, and C.W. Oosterlee, Numerical Linear Algebra with
Applications, 17:871894, 2010.
Adaptive reductionbased
multigrid for nearly singular and highly disordered physical systems, J. Brannick, A. Frommer, K. Kahl,
S. MacLachlan, and L. Zikatanov, Electronic Transactions on
Numerical Analysis, 37:276295, 2010.
A Comparison of TwoLevel Preconditioners
based on Multigrid and Deflation, J.M. Tang, S.P. MacLachlan,
R. Nabben, and C. Vuik, SIAM J. Matrix Anal. Appl., 31:17151739, 2010.
An angular multigrid method for monoenergetic
particle beams in Flatland, C. Börgers and
S. MacLachlan, J. Comp. Phys., 229:29142931, 2010.
Scalable robust solvers for unstructured FE modeling applications;
solving the Stokes equation for models with large, localized
viscosity contrasts, T. Geenen, M. ur Rehman, S.P. MacLachlan,
G. Segal, C. Vuik, A.P. van den Berg, and
W. Spakman, Geochemistry, Geophysics, Geosystems, 10(9), 2009.
A multigridbased shiftedLaplacian
preconditioner for a fourthorder Helmholtz discretization,
N. Umetani, S.P. MacLachlan, and C.W. Oosterlee, Numerical Linear
Algebra with Applications, 16:603626, 2009.
Fast and robust solvers for pressure
correction in bubbly flow problems, S.P. MacLachlan, J.M. Tang,
and C. Vuik, J. Comp. Phys.,
227:97429761, 2008.
Algebraic multigrid solvers for
complexvalued matrices, S.P. MacLachlan and C.W. Oosterlee, SIAM J. Sci. Comp.,
30:15481571, 2008.
Greedy coarsening strategies for
nonsymmetric problems, S. MacLachlan and Y. Saad, SIAM J. Sci. Comp.,
29:21152143, 2007.
A greedy strategy for coarsegrid
selection, S. MacLachlan and Y. Saad, SIAM J. Sci. Comp.,
29:18251853, 2007.
Adaptive reductionbased AMG,
S. MacLachlan, T. Manteuffel, and S. McCormick, Numerical Linear
Algebra with Applications, 13:599620, 2006.
An energybased AMG coarsening strategy
, J. Brannick, M.
Brezina, S.
MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge,
Numerical Linear Algebra with Applications, 13:133148
2006.
Multilevel upscaling through
variational
coarsening, S.P. MacLachlan and J.D. Moulton, Water Resources
Research, 42, 2006.
Adaptive algebraic multigrid, M.
Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J.
Ruge, SIAM
J. Sci. Comp., 27:12611286, 2006.
Adaptive smoothed aggregation (aSA)
multigrid, M.
Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J.
Ruge, SIAM Review,
47:317346, 2005.
Adaptive smoothed aggregation (aSA), M.
Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J.
Ruge, SIAM J. Sci. Comp., 25:18961920, 2004.
Refereed Proceedings:
Adaptive smoothed aggregation in Lattice
QCD, J. Brannick, M.
Brezina, D. Keyes, O. Livne, I. Livshits, S.
MacLachlan, T. Manteuffel, S. McCormick, J. Ruge, and L. Zikatanov,
pages 505512 in Domain Decomposition Methods in Science and
Engineering XVI, Lecture Notes in Computational Science and
Engineering, Springer, 2007.
PhD Thesis:
Improving robustness in multiscale
methods, S. MacLachlan, PhD Thesis, July 2004.
Other:
An energyminimization finiteelement approach for the FrankOseen model of nematic liquid crystals: continuum and discrete analysis, J. H. Adler, T. J. Atherton, D. B. Emerson, and S. P. MacLachlan, technical report, 2014; also available at arXiv.org.
Robust solution of singularly perturbed
problems using multigrid methods; analysis and numerical results in one and two dimensions, S. MacLachlan and N. Madden,
technical report, 2012.
Scalable robust solvers for unstructured FE geodynamic
modeling applications;
solving the Stokes equation for models with large localized viscosity
contrasts in 3D
spherical domains,
T. Geenen, M. ur Rehman, S. P. MacLachlan, G. Segal, C. Vuik,
A. P. van den Berg, and
W. Spakman, V European Conference on Computational Fluid
Dynamics ECCOMAS CFD
2010, 2010.
Local postprocessing for locally conservative fluxes in
the Galerkin method for groundwater flows,
E.T. Coon, S.P. MacLachlan, and J.D. Moulton, Los Alamos National
Laboratory Technical Report LAUR 0908292, 2009.
Contaminant transport in municipal water
systems,
S. Ali et al., Proceedings of the 3rd PIMS
Industrial Problem Solving Workshop, Victoria, BC, June 1999.
