Research Overview


Angular Multigrid and Particle Transport
In collaboration with: Christoph Börgers, Tufts University

Related Papers and Presentations:
  • An angular multigrid method for monoenergetic particle beams in Flatland, C. Börgers and S. MacLachlan, in preparation, 2008.



    • Local Fourier Analysis for systems of PDEs
    In collaboration with: Kees Oosterlee, TU-Delft

    Related Papers and Presentations:
  • Fourier analysis of multigrid applied to systems of PDEs, S.P. MacLachlan and C.W. Oosterlee, in preparation, 2008.
  • April 10, 2008: Copper Mountain Conference on Iterative Methods, abstract , slides (.pdf)



    • Multigrid Methods for Stretched Grids
    In collaboration with: Hisham bin Zubair, Kees Oosterlee, TU-Delft

    Related Papers and Presentations:



    Multigrid Methods for Quantum Chromodynamics
    In collaboration with James Brannick, Ludmil Zikatanov, Penn State University, Karsten Kahl, Andreas Frommer, BU-Wuppertal

    Related Papers and Presentations:
  • 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.
  • Reduction-based AMG methods for lattice quantum chromodynamics, J. Brannick, A. Frommer, K. Kahl, S. MacLachlan, and L. Zikatanov, in preparation, 2008.
  • April 26, 2007: Rutherford Appleton Laboratory Computational Mathematics and Applications Seminar, abstract , slides (.pdf)
  • May 16, 2007: Los Alamos National Laboratory SWG invited talk, abstract , slides (.pdf)



    • Multiscale Methods for Flow through Porous Media
    In collaboration with Ethan Coon, Columbia University, J. David Moulton, Los Alamos National Laboratory

    Related Papers and Presentations:
  • Multilevel upscaling through variational coarsening, S.P. MacLachlan and J.D. Moulton, Water Resources Research, 42, 2006.
  • March 19, 2003: SIAM Mathematical and Computational Issues in the Geosciences conference - abstract , slides (.pdf)
  • Computing continuous velocity fields in heterogeneous porous media, E.T. Coon, S.P. MacLachlan, and J.D. Moulton, in preparation, 2008.
  • July 26, 2002: Los Alamos National Laboratory Student Seminar, abstract, slides (.pdf)
  • September 22, 2004: Third DOE Workshop on Multiscale Mathematics, abstract , slides (.pdf)
  • April 24, 2006: Math seminar, Boise State University - abstract , slides (.pdf)



    • Theory-based Algebraic Multigrid Methods
    In collaboration with James Brannick, Ludmil Zikatanov, Penn State University, Luke Olson, University of Illinois

    Related Papers and Presentations:
  • Practical aspects of theoretical bounds for algebraic multigrid performance, S. MacLachlan and L. Olson, in preparation, 2008.
  • July 20, 2007: 6th International Congress on Industrial and Applied Mathematics, abstract , slides (.pdf)



    • Comparison of Multilevel Preconditioners
    In collaboration with Jok Tang, Kees Vuik, TU-Delft, Reinhard Nabben, TU-Berlin

    Related Papers and Presentations:
  • 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.
  • 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.
  • March 19, 2008: Computational and Applied Mathematics Colloquium, Penn State University, slides (.pdf)



    • Multigrid Preconditioners for the Helmholtz Equation
    In collaboration with Nobuyuki Umetani, Tokyo University, Kees Oosterlee, TU-Delft

    Related Papers and Presentations:
  • Algebraic multigrid solvers for complex-valued matrices, S.P. MacLachlan and C.W. Oosterlee, SIAM J. Sci. Comp., to appear, 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.
  • March 22, 2007: Copper Mountain Conference on Multigrid Methods, abstract , slides (.pdf)
  • May 23, 2007: CAIMS*SCMAI 2007 Meeting, abstract , slides (.pdf)



    • Multilevel Block Factorizations and ILUT
    In collaboration with Yousef Saad, University of Minnesota

    Related Papers and Presentations:
  • General strategies for modification of threshold-based incomplete factorizations, S. MacLachlan and Y. Saad, in preparation, 2008.



    • Algebraic Multigrid Coarsening
    In collaboration with Marian Brezina, Tom Manteuffel, Steve McCormick, John Ruge, CU-Boulder, James Brannick, Penn State University, Yousef Saad, University of Minnesota

    Related Papers and Presentations:
  • 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.
  • A greedy strategy for coarse-grid selection, S. MacLachlan and Y. Saad, SIAM J. Sci. Comp., 29:1825-1853, 2007.
  • Greedy coarsening strategies for non-symmetric problems, S. MacLachlan and Y. Saad, SIAM J. Sci. Comp., 29:2115-2143, 2007.
  • April 5, 2005: Copper Mountain Conference on Multigrid Methods, abstract , slides (.pdf)
  • February 20, 2006: CSE seminar, UIUC, abstract , slides (.pdf)
  • April 4, 2006: Copper Mountain Conference on Iterative Methods, abstract , slides (.pdf)
  • June 16, 2006: Sparse Days at CERFACS, Toulouse, abstract , slides (.pdf)
  • July 3, 2007: System Simulation Group Seminar, University Erlangen-Nuremberg, slides (.pdf)



    • Adaptive Algebraic Multigrid Methods
    In collaboration with Marian Brezina, Tom Manteuffel, Steve McCormick, John Ruge, CU-Boulder, Rob Falgout, Lawrence Livermore National Laboratory

    Related Papers and Presentations:
  • 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.
  • 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 algebraic multigrid, M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, SIAM J. Sci. Comp., 27:1261-1286, 2006.
  • Adaptive reduction-based AMG, S. MacLachlan, T. Manteuffel, and S. McCormick, Numerical Linear Algebra with Applications, 13:599-620, 2006.
  • March 28, 2002: Copper Mountain Conference on Iterative Methods, abstract , slides (.pdf )
  • September 30, 2002: Comprehensive Exam, abstract , paper (.ps.gz) , paper (.pdf) , slides (.pdf)
  • February 11, 2003: SIAM conference on Computational Science and Engineering, abstract , poster (.pdf), Received SIAM travel grant to attend this meeting
  • April 2, 2003: Copper Mountain Conference on Multigrid Methods - abstract, slides (.pdf), Winner in the Student Paper Competition: paper (.ps.gz), paper (.pdf)
  • April 24, 2003: SCV Seminar, UBC, abstract , slides (.pdf)
  • June 20, 2003: SIAM Annual Meeting, abstract , slides (.pdf)
  • August 6, 2003: PIMS Workshop on Numerical Linear Algebra and Applications - abstract , slides (.pdf)
  • March 31, 2004: Copper Mountain Conference on Iterative Methods - abstract (.pdf) , slides (.pdf )
  • May 18, 2004: CU Thesis Defense - abstract , slides (.pdf)
  • February 15, 2005: SIAM conference on Computational Science and Engineering, abstract , slides (.pdf), Talk in minisymposium: Enhancing Multigrid Performance by Compatible Relaxation and Self-Adaptation
  • May 5, 2005: Seventh IMACS International Symposium on Iterative Methods in Scientific Computing, abstract , slides (.pdf), Organizer of minisymposia: Recent Advances in Multilevel Methods
  • June 21, 2006: DCSE seminar, TU-Delft, abstract , slides (.pdf)
  • December 12, 2006: MAS Scientific Computing seminar, CWI, Amsterdam - slides (.pdf)
  • September 6, 2007: Scientific Computing Group Seminar, University of Wuppertal, slides (.pdf)