Research: Currently, I am investigating the development
of efficient multigrid preconditioners for problems with
complex-valued coefficients, including frequency-domain wave
propagation and quantum chromodynamics. This work is in
collaboration with Kees Oosterlee of TU-Delft and with
Shell.
Previously, I was a postdoctoral researcher at both the
University of Minnesota and the University of Colorado at
Boulder. At UMN, I worked with Yousef Saad on additive
multilevel preconditioners based on incomplete factorizations.
We developed a new coarse-grid selection algorithm that offers
provable optimality of the resulting (two-level)
preconditioners. As a postdoc at CU, I worked with Steve
McCormick and Tom Manteuffel on adaptive algebraic multigrid
methods, extending the approaches developed in my thesis. We
proposed a new coarsening algorithm based on local measures of
the performance of relaxation within a multigrid method, and
applied the adaptive smoothed aggregation algorithm to a set of
matrices that arise in lattice gauge theory from quantum
chromodynamics.
In collaboration with David Moulton from Los Alamos National
Laboratory (and, more recently, with Ethan Coon from Columbia
University), I have also been working on developing a multiscale
modelling framework based on variational multigrid principles.
This technique may be viewed as one for numerical homogenization
or upscaling, or as a model-order reduction scheme, centred on
the algebraic coarsening of finite element models. We have
demonstrated effective reduction of dimension in 2D models by a
factor of 1024 (a factor of 32 in each direction) and are
currently applying this technique to models of unsaturated and
multiphase fluid flow through porous media.
As a Ph.D. student at the University of Colorado at Boulder, I
was a member of the team that developed the adaptive multigrid
methodology. This extension to algebraic multigrid methods is
aimed at linear systems which have properties that make them
amenable to effective multigrid solution, but for which the
necessary details of these properties are unknown, or too
expensive to find out. This research led to several
publications, including being selected to appear in the SIAM
Review, and continues to be an active area of research.
For more information on any of the above topics, please see my
(now out of date)
research statement or
list of publications (below).
My undergraduate thesis at the University of British
Columbia focused on the evaluation of a set of oscillatory
integrals that arise in analytic techniques for electrical
impedance tomography. This research was supervised by Anthony
Peirce and Richard Froese at UBC, but unfortunately I no longer
have an electronic copy of it.
Publications:
Computing continuous velocity fields in heterogeneous porous media,
E.T. Coon, S.P. MacLachlan, and J.D. Moulton, in preparation, 2007.
Practical aspects of theoretical bounds for algebraic multigrid performance,
S. MacLachlan and L. Olson, in preparation, 2007.
General strategies for modification of threshold-based incomplete factorizations,
S. MacLachlan and Y. Saad, in preparation, 2007.
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.,
to appear, 2007.
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 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.
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.
Improving robustness in multiscale
methods, S. MacLachlan, PhD Thesis, July 2004.
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.
Contaminant transport in municipal
water systems,
in Proceedings of the 3rd PIMS Industrial Problem Solving Workshop,
Victoria, BC, June 1999.
Recent Work and Talks:
September 6, 2007: Scientific Computing Group Seminar, University of Wuppertal - slides (.pdf)
July 20, 2007: 6th International Congress on Industrial and Applied Mathematics -
abstract
, slides (.pdf)
July 3, 2007: System Simulation Group Seminar, University Erlangen-Nuremberg - slides (.pdf)
May 23, 2007: CAIMS*SCMAI 2007 Meeting -
abstract
, slides (.pdf)
May 16, 2007: Los Alamos National Laboratory SWG invited talk -
abstract
, slides (.pdf)
April 26, 2007: Rutherford Appleton Laboratory Computational
Mathematics and Applications Seminar -
abstract
, slides (.pdf)
March 22, 2007: Copper Mountain Conference on Multigrid Methods -
abstract
, slides (.pdf)
December 12, 2006: MAS Scientific Computing seminar, CWI, Amsterdam -
slides (.pdf)
June 21, 2006: DCSE seminar, TU-Delft - abstract , slides (.pdf)
June 16, 2006: Sparse Days at CERFACS, Toulouse - abstract , slides (.pdf)
April 24, 2006: Math seminar, Boise State University - abstract , slides (.pdf)
April 4, 2006: Copper Mountain Conference on Iterative Methods -
abstract
, slides (.pdf)
February 20, 2006: CSE seminar, UIUC - abstract , slides (.pdf)
May 5, 2005:
Seventh IMACS International Symposium on
Iterative Methods in Scientific Computing -
abstract
, slides (.pdf)
Organizer of minisymposia: Recent Advances in Multilevel Methods
April 5, 2005: Copper Mountain Conference on Multigrid Methods -
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
September 22, 2004: Third DOE Workshop on Multiscale Mathematics - abstract , slides (.pdf)
May 18, 2004: CU Thesis Defense - abstract , slides (.pdf)
March 31, 2004: Copper Mountain Conference on Iterative Methods -
abstract (.pdf)
, slides (.pdf
)
August 6, 2003: PIMS Workshop on Numerical Linear Algebra and Applications
- abstract , slides (.pdf)
June 20, 2003: SIAM
Annual Meeting -
abstract
, slides (.pdf)
Session Chair for CP13, Numerical PDEs
April 24, 2003: SCV Seminar, UBC - abstract , slides (.pdf)
April 2, 2003: Copper Mountain Conference on Multigrid Methods - abstract, slides (.pdf), paper (.ps.gz), paper (.pdf)
Winner in the Student Paper Competition
March 19, 2003: SIAM
Mathematical and Computational Issues in the Geosciences conference -
abstract
, slides (.pdf)
Session Chair for CP17, Multiscale Modelling
February 11,
2003: SIAM conference on Computational Science and
Engineering -
abstract
, poster (.pdf)
Received SIAM travel grant to attend this meeting
October 17, 2002: SIAM club Student Seminar -
abstract
, slides (.pdf)
September
30, 2002: Comprehensive Exam -
abstract
, paper (.ps.gz)
, paper (.pdf)
, slides (.pdf)
July 26, 2002: Los Alamos National Laboratory Student Seminar - abstract,
slides (.pdf)
April 30, 2002: Applied Math Grad Student Seminar -
abstract
, slides (.pdf)
March 28, 2002: Copper Mountain Conference on Iterative Methods -
abstract
, slides (.pdf
)
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