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Scott MacLachlan


scott.maclachlan [at] tufts.edu

Department of Mathematics
Tufts University
Bromfield-Pearson Building
503 Boston Avenue
Medford, MA 02155
617-627-2356



In July 2014, I will move to the Department of Mathematics and Statistics at Memorial University of Newfoundland, in St. John's, NL, Canada.

       Research        Publications        Teaching        Personal


Research Overview

My research interests are in computational applied mathematics and scientific computation. In particular, I work on developing efficient numerical methods for the solution of partial differential and integro-differential equations, using the tools of multiscale numerical analysis.



Publications
In preparation:

  • Non-Hermitian coarsening strategies for algebraic multigrid, S. MacLachlan.

  • Implied volatility and the risk-free rate of return in options markets, M. Bianconi, S. MacLachlan, and M. Sammon, January 2014.

    Journal Articles:
  • An energy-minimization finite-element approach for the Frank-Oseen 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):194-220, 2014.

  • Local Fourier analysis of space-time relaxation and multigrid schemes, S. Friedhoff, S. MacLachlan and C. Börgers, SIAM J. Sci. Comput., 35:S250-276, 2013.

  • Robust solution of singularly perturbed problems using multigrid methods, S. MacLachlan and N. Madden, SIAM J. Sci. Comput., 35:A2225-A2254, 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, 50:321-333, 2012.

  • Modification and compensation strategies for threshold-based incomplete factorizations, S. MacLachlan, D. Osei-Kuffuor, and Y. Saad, SIAM J. Sci. Comput., 34:A48-A75, 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, 19:389-413, 2012.

  • Iterative parameter choice and algebraic multigrid for anisotropic diffusion denoising, D. Chen, S. MacLachlan, and M. Kilmer, SIAM J. Sci. Comp., 33:2972-2994, 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, 18:751-774, 2011.

  • A fast method for the solution of the Helmholtz equation, E. Haber and S. MacLachlan, J. Comp. Phys., 230(12):4403-4418, 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):1180-1200, 2011.

  • A geometric multigrid method based on L-shaped coarsening for PDEs on stretched grids, H. bin Zubair, S.P. MacLachlan, and C.W. Oosterlee, Numerical Linear Algebra with Applications, 17:871-894, 2010.

  • Adaptive reduction-based 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, 37:276-295, 2010.

  • A Comparison of Two-Level Preconditioners based on Multigrid and Deflation, J.M. Tang, S.P. MacLachlan, R. Nabben, and C. Vuik, SIAM J. Matrix Anal. Appl., 31:1715-1739, 2010.

  • An angular multigrid method for monoenergetic particle beams in Flatland, C. Börgers and S. MacLachlan, J. Comp. Phys., 229:2914-2931, 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 multigrid-based shifted-Laplacian preconditioner for a fourth-order Helmholtz discretization, N. Umetani, S.P. MacLachlan, and C.W. Oosterlee, Numerical Linear Algebra with Applications, 16:603-626, 2009.

  • Fast and robust solvers for pressure correction in bubbly flow problems, S.P. MacLachlan, J.M. Tang, and C. Vuik, J. Comp. Phys., 227:9742-9761, 2008.

  • Algebraic multigrid solvers for complex-valued matrices, S.P. MacLachlan and C.W. Oosterlee, SIAM J. Sci. Comp., 30:1548-1571, 2008.

  • Greedy coarsening strategies for non-symmetric problems, S. MacLachlan and Y. Saad, SIAM J. Sci. Comp., 29:2115-2143, 2007.

  • A greedy strategy for coarse-grid selection, S. MacLachlan and Y. Saad, SIAM J. Sci. Comp., 29:1825-1853, 2007.

  • Adaptive reduction-based AMG, S. MacLachlan, T. Manteuffel, and S. McCormick, Numerical Linear Algebra with Applications, 13:599-620, 2006.

  • An energy-based AMG coarsening strategy , J. Brannick, M. Brezina, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, Numerical Linear Algebra with Applications, 13:133-148 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., 27:1261-1286, 2006.

  • Adaptive smoothed aggregation (aSA) multigrid, M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, SIAM Review, 47:317-346, 2005.

  • Adaptive smoothed aggregation (aSA), M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, SIAM J. Sci. Comp., 25:1896-1920, 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 505-512 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 energy-minimization finite-element approach for the Frank-Oseen 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 post-processing 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 LA-UR 09-08292, 2009.

  • Contaminant transport in municipal water systems, S. Ali et al., Proceedings of the 3rd PIMS Industrial Problem Solving Workshop, Victoria, BC, June 1999.



  • Teaching Overview
    Fall 2013:
  • Math 87, Mathematical Modeling and Computing

    Spring 2013:
  • Math 250-01, Numerical Methods for PDEs
  • Math 250-04, Seminar in Computational and Applied Mathematics

    Fall 2012:
  • Math 250-03, Linear Partial Differential Equations
  • Math 87, Mathematical Modeling and Computing

    Spring 2012:
  • Math 250-02, Classic Papers in Applied Mathematics
  • Math 13, Calculus III

    Fall 2011:
  • Math 50-02, Mathematical Modeling and Computing
  • Math 13, Calculus III

    Spring 2010:
  • Math 250-03, Numerical Methods for PDEs
  • Math 13, Calculus III

    Fall 2009:
  • Math 135, Real Analysis I
  • Math 13, Calculus III

    Spring 2009:
  • Math 136, Real Analysis II
  • Math 38, Differential Equations

    Fall 2008:
  • Math 135, Real Analysis I
  • Math 38, Differential Equations

    Spring 2008:
  • Math 38, Differential Equations

    Past Courses:
  • WI4145, Computational Science and Engineering, TU-Delft
  • APPM 7400, Topics in Applied Mathematics: Multigrid Methods, CU-Boulder
  • Lead Teaching Assistant, Department of Applied Mathematics, CU-Boulder
  • GEEN 1350, Calculus I Workgroup, CU-Boulder
  • APPM 2350, Calculus III, CU-Boulder
  • Math 100, Calculus I, UBC

    Other:
  • SIAM student chapter lecture on the post-doctoral job search, April 14, 2008, slides (.pdf)
  • Tufts Mathematical Contest in Modeling team
  • 2009 BGCE Student Prize Committee


  • Personal

    My wife, Alison, and I both originate from the Vancouver area of western Canada, where we still enjoy passing time between the ocean and the mountains. We're now learning to love the other coast, and are excited to start exploring.

    When I'm not doing math, I spend most of my time outdoors, hiking, biking, paddling, or otherwise enjoying some fresh air. I can also often be spotted curled up with a good book, or the Sunday crossword puzzle.

    The design of this page was stolen (with permission) from Chad Westphal.