In preparation:
NonHermitian coarsening strategies for algebraic multigrid, S. MacLachlan.
Journal Articles:
Multigrid reductionintime convergence for advection problems: A Fourier analysis perspective, H. De Sterck, S. Friedhoff, O.A. Krzysik, S.P. MacLachlan, submitted, 2022
Finiteelement discretization of the smectic density equation, P.E. Farrell, A. Hamdan, S.P. MacLachlan, submitted, 2022
Monolithic multigrid for implicit RungeKutta discretizations of incompressible fluid flow, R. AbuLabdeh, S. MacLachlan, and P.E. Farrell, in revision, 2022
CoarseGrid Selection Using Simulated Annealing, T.U. Zaman, S.P. MacLachlan, L.N. Olson, and M. West, revised, 2022
Multigrid reduction in time for nonlinear hyperbolic equations, F. Danieli and S. MacLachlan, Electronic Transactions on Numerical Analysis 58:4365, 2023.
Learning Interface Conditions in Domain Decomposition Solvers, A. Taghibakhshi, N. Nytko, T. Zaman, S. MacLachlan, L. Olson, and M. West, to appear, NeurIPS 2022
A new mixed finiteelement method for H2 elliptic problems, P.E. Farrell, A. Hamdan, and S. MacLachlan, to appear, Computers and Mathematics with Applications, 2022.
Monolithic multigrid for a reducedquadrature discretization of poroelasticity, J.H. Adler, Y. He, X. Hu, S. MacLachlan, and P. Ohm, to appear, SIAM J. Sci. Comp., 2022
A BoundaryLayer Preconditioner for Singularly Perturbed Convection Diffusion, S.P. MacLachlan, N. Madden, and T.A. Nhan, SIAM Journal on Matrix Analysis and Applications, 43(2):561583, 2022
Loworder preconditioning of the Stokes equations, A. Voronin, Y. He, S. MacLachlan, L. Olson, and R. Tuminaro, Numerical Linear Algebra with Applications 29(3):e2426, 2022.
OptimizationBased Algebraic Multigrid Coarsening Using Reinforcement Learning, A. Taghibakhshi, S. MacLachlan, L. Olson, and M. West, Advances in Neural Information Processing Systems 34 (NeurIPS 2021), 34:1212912140, 2021
Selective decay for the rotating shallowwater equations with a structurepreserving discretization, R. Brecht, W. Bauer, A. Bihlo, F. GayBalmaz, and S. MacLachlan, Physics of Fluids 33, 116604 (2021)
Optimizing MGRIT and Parareal coarsegrid operators for linear advection, H. De Sterck, R.D. Falgout, S. Friedhoff, O.A. Krzysik, S.P. MacLachlan, Numerical Linear Algebra with Applications, 28(4):e2367, 2021.
Monolithic multigrid for magnetohydrodynamics, J.H. Adler, T. Benson, E.C. Cyr, P.E. Farrell, S. MacLachlan, and R. Tuminaro, SIAM J. Sci. Comp., 43(5):S70S91, 2021.
Structural Landscapes in Geometrically Frustrated Smectics, J. Xia, S. MacLachlan, T.J. Atherton, and P.E. Farrell, Phys. Rev. Lett. 126, 177801 (2021).
Numerical modeling of a memorybased diffusivity equation and determination of its fractional order value, T.U. Zaman, S. MacLachlan, and M.E. Hossain, Computational Geosciences, 25:655669, 2021.
A local Fourier analysis of additive Vanka relaxation for the Stokes equations, P.E. Farrell, Y. He, and S. MacLachlan, Numerical Linear Algebra with Applications, 28(3):e2306, 2021.
Tuning Multigrid Methods with Robust Optimization,
J. Brown, Y. He, S. MacLachlan, M. Menickelly, S.M. Wild, SIAM J. Sci. Comp., 43(1):A109A138, 2021.
Block preconditioning techniques for geophysical electromagnetics, H. bin Zubair Syed, C. Farquharson, and S. MacLachlan, SIAM J. Sci. Comp., 42(3):B696B721, 2020.
Goaloriented hradaptivity for finiteelement models with jumping coefficients, H. Jahandari, S. MacLachlan, R. Haynes, and N. Madden, Computational Geosciences, 24:12571283, 2020.
Twolevel Fourier analysis of multigrid for higherorder finiteelement discretizations of the Laplacian, Y. He and S. MacLachlan, Numerical Linear Algebra with Applications, 27(3): e2285, 2020.
Firstorder system least squares finiteelements for singularly perturbed reactiondiffusion equations, James H. Adler, Scott MacLachlan, and Niall Madden, LargeScale Scientific Computing 2019, Springer, Lecture Notes in Computer Science vol. 11958, pp. 314, 2020.
Convergence analysis for parallelintime solution of hyperbolic systems, H. De Sterck, S. Friedhoff, A. J. M. Howse, and S. P. MacLachlan, Numerical Linear Algebra with Applications, 27(1):e2271, 2020.
Multistage cooling and freezing of a saline spherical water droplet, A. DehghaniSanij, S. MacLachlan, G. Naterer, Y. Muzychka, R. Haynes, and V. Enjilela, International Journal of Thermal Sciences, 147:106095, 2020.
Local Fourier analysis of BDDClike algorithms, J. Brown, Y. He, and S. MacLachlan, SIAM J. Sci. Comput., 41(1):S346S369, 2019.
Local Fourier analysis for mixed finiteelement methods for the Stokes equations, Y. He and S. MacLachlan, Journal of Computational and Applied Mathematics, 357:161183, 2019.
Variational integrator for the rotating shallowwater equations on the sphere, R. Brecht, W. Bauer, A. Bihlo, F. GayBalmaz, and S. MacLachlan, Quarterly Journal of the Royal Meteorological Society, 145(720):10701088, 2019.
Vectorpotential finiteelement formulations for twodimensional resistive magnetohydrodynamics, J.H. Adler, Y. He, X. Hu, and S.P. MacLachlan, Computers and Mathematics with Applications, 77(2):476493, 2019
Parallelintime multigrid with adaptive spatial coarsening for the linear advection and inviscid Burgers equations, H. De Sterck, R. Falgout, A. Howse, S. MacLachlan, and J. Schroder, SIAM J. Sci. Comput., 41(1):A538565, 2019.
Wellbalanced meshbased and meshless schemes for the shallowwater equations, A. Bihlo and S. MacLachlan, BIT Numerical Mathematics, 58(3):579598, 2018.
Boundary layer preconditioners for finiteelement discretizations of singularly perturbed reactiondiffusion problems, T.A. Nhan, S. MacLachlan, and N. Madden, Numerical Algorithms, 79:281310, 2018.
Local Fourier analysis of blockstructured multigrid relaxation schemes for the Stokes equations, Y. He and S. MacLachlan, Numerical Linear Algebra with Applications, 25(3):e2147, 2018.
A wellbalanced meshless tsunami propagation and inundation model, R. Brecht, A. Bihlo, S. MacLachlan, and J. Behrens, Advances in Water Resources, 115:273285, 2018.
Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms, D.B. Emerson, P.E. Farrell, J.H. Adler, S.P. MacLachlan, and T.J. Atherton, Liquid Crystals, 45(3):341350, 2018.
Discrete energy laws for the firstorder system leastsquares finiteelement approach, J. H. Adler, I. Lashuk, S. P. MacLachlan, and L. T. Zikatanov, LargeScale Scientific Computing 2017, Springer, Lecture Notes in Computer Science, vol. 10665, pp. 320, 2018
Compositegrid multigrid for diffusion on the sphere, J.H. Adler, I. Lashuk, and S.P. MacLachlan, Numerical Linear Algebra with Applications, 25(1):e2115, 2018
Multigrid methods with spacetime concurrency, R. Falgout, S. Friedhoff, Tz. Kolev, S. MacLachlan, J. Schroder, and S. Vandewalle, Comput. Vis. Sci., 18(45):123143, 2017.
A Gauged Finiteelement Potential Formulation for Accurate Inductive and Galvanic Modelling of Threedimensional Electromagnetic Problems, S.M. Ansari, C.G. Farquharson, and S.P. MacLachlan, Geophysical Journal International, 210(1):105129, 2017
Preconditioning a massconserving discontinuous Galerkin discretization of the Stokes Equations, J. Adler, T. Benson, and S. MacLachlan, Numer. Linear Alg. Appl., 24(3):e2047, 2017
Effect of thermocapillary stress on slip length for a channel textured with parallel ridges, M. Hodes, T. Kirk, G. Karamanis, and S. MacLachlan, Journal of Fluid Mechanics, 814:301324, 2017.
A deflation technique for detecting multiple liquid crystal equilibrium states, J.H. Adler, D.B. Emerson, P.E. Farrell, and S.P. MacLachlan, SIAM J. Sci. Comp., 39(1):B29B52, 2017.
Effect of meniscus curvature on apparent thermal slip, L. Steigerwalt Lam, M. Hodes, G. Karmanis, T. Kirk, and S. MacLachlan, Journal of Heat Transfer, 138(12):122004, 2016.
A firstorder system PetrovGalerkin
discretisation for a reactiondiffusion problem on a fitted mesh,
J. Adler, S. MacLachlan, and N. Madden, IMA J. Numer. Anal., 36(3):12811309, 2016
Constrained optimization for liquid crystal equilibria, J. H. Adler, D. B. Emerson, S. P. MacLachlan, and T. A. Manteuffel, SIAM J. Sci. Comp., 38(1):B50B76, 2016
Monolithic multigrid methods for twodimensional resistive magnetohydrodynamics, J. H. Adler, T. R. Benson, E. C. Cyr, S. P. MacLachlan, and R. S. Tuminaro, SIAM J. Sci. Comp., 38(1):B1B24, 2016
Energy minimization for liquid crystal
equilibrium with electric and flexoelectric effects, J. H. Adler,
T. J. Atherton, T. R. Benson, D. B. Emerson, and S. P. MacLachlan, SIAM J. Sci. Comp., 37(5):S157S176, 2015.
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, SIAM J. Numer. Anal., 53(5):22252254, 2015.
A generalized predictive analysis tool for
multigrid methods, S. Friedhoff and S. MacLachlan, Numer. Linear Alg. Appl., 22:618647, 2015.
Effect of evaporation and condensation at menisci on apparent
thermal slip, M. Hodes, L. Steigerwalt Lam, A. Cowley, S. MacLachlan, and
R. Enright, Journal of Heat Transfer, 137(7):071502, 2015
Implied volatility and the riskfree rate of return in options markets, M. Bianconi, S. MacLachlan, and M. Sammon, North American Journal of Economics and Finance, 31:126, 2015.
Parallel time integration with
multigrid, R.D. Falgout, S. Friedhoff, Tz.V. Kolev,
S.P. MacLachlan, and J.B. Schroder, SIAM J. Sci. Comput., 36:C625C661, 2014.
Mathematical and computational
models of incompressible materials subject to shear, J.H. Adler,
L. Dorfmann, D. Han, S. MacLachlan, and C. Paetsch,
IMA Journal of Applied Mathematics, 79(5):889914, 2014.
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:
Isoperimetric relations between Dirichlet and Neumann eigenvalues, G. Cox, S. MacLachlan, and L. Steeves, 2020.
The role of energy minimization in algebraic multigrid interpolation, J. Brannick, S. MacLachlan, J. Schroder, and B. Southworth, 2019.
Constrained optimization for liquid crystal equilibria: extended results, J. H. Adler, D. B. Emerson, S. P. MacLachlan, and T. A. Manteuffel, technical report, 2014; also available at arXiv.org.
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.
