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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


       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. Click here for a description of some of my past and current research efforts.



Publications
In preparation:

  • Computing continuous velocity fields in heterogeneous porous media, E.T. Coon, S.P. MacLachlan, and J.D. Moulton, 2008.

  • Practical aspects of theoretical bounds for algebraic multigrid performance, S. MacLachlan and L. Olson, 2008.

  • General strategies for modification of threshold-based incomplete factorizations, S. MacLachlan and Y. Saad, 2008.

  • An angular multigrid method for monoenergetic particle beams in Flatland, C. Börgers and S. MacLachlan, 2008.

  • Reduction-based AMG methods for lattice quantum chromodynamics, J. Brannick, A. Frommer, K. Kahl, S. MacLachlan, and L. Zikatanov, 2008.

  • Fourier analysis of multigrid applied to systems of PDEs, S.P. MacLachlan and C.W. Oosterlee, 2008.

    Journal Articles:
  • 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., submitted, 2008.

  • 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, submitted, 2008.

  • Fast and robust solvers for pressure correction in bubbly flow problems, S.P. MacLachlan, J.M. Tang, and C. Vuik, J. Comp. Phys., submitted, 2007.

  • 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.



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

    Currently:
  • 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)


  • 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.