Ed Bueler's Research
My interests include ice flow, partial differential equations, variational inequalities, and the numerical analysis thereof including the PETSc, Firedrake and PISM open source software projects.
Book and book chapter
- E. Bueler, PETSc for Partial Differential Equations: Numerical Solutions in C and Python, SIAM Press 2021. Supporting codes at github.com/bueler/p4pdes.
- E. Bueler, "Chapter 8. Numerical modeling of ice sheets, streams, and shelves," in Glaciers and Ice Sheets in the Climate System: The Karthaus Summer School Lecture Notes, A. Fowler and F. Ng editors, Springer 2021
Papers in applied mathematics: numerical ice sheet modeling
See my current CV (PDF) for this still-growing set of papers.
Papers in applied mathematics: delay differential equations and their
- E. A. Butcher, M. Sari, E. Bueler,
and T. Carlson (2009). Magnus' expansion for time-periodic
systems: parameter-dependent approximations, Commun.
Nonlinear Sci. Numer. Simulat. 14,
- E. A. Butcher, O. A. Bobrenkov, E.
Bueler, and P. Nindujarla (2009). Analysis of milling stability by the
Chebyshev collocation method: Algorithm and optimal stable immersion
levels, J. Comput. Nonlinear Dynam. 4
- V. Deshmukh, E.A. Butcher, and E.
Bueler (2008). Dimensional reduction of nonlinear delay
differential equations with periodic coefficients using Chebyshev
spectral collocation, Nonlinear Dynamics 52,
- E. Bueler (2007). Error bounds for approximate eigenvalues
of periodic-coefficient linear delay differential equations,
SIAM J. Num. Analysis 45 (6),
- E. A. Butcher, H. Ma, E. Bueler,
V. Averina, and Z. Szabo (2004), Stability
equations via Chebyshev polynomials, Int. J. Numer.
Meth. Engng. 59, 895--922.
- E. A. Butcher, H. Ma, and E. Bueler
of linear dynamic systems with time delay and periodic coefficients
under control excitations, J. Dynamic Systems, Measurement
and Control (Trans. ASME), 125, 236--243.
Papers in mathematics
Bueler (1999) was my
thesis. See Erratum
for Theorem 3.4: PDF
. Confirmation of conjecture
6.3, the second of three in the paper, appears in Gong
& Wang (2001), Quart. J. Math
. A counterexample to my
conjecture 1.1 was given by G.
Carron (2007), Proc. AMS
. Conjecture 1.1 should have added the
tame" (i.e. M
is homeomorphic to
the interior of a compact manifold with boundary), the hypothesis
considered in Bueler & Prokhorenkov (2002)
Reviewed conference proceedings, commentaries, and short notes
- W. Lipscomb, R. Bindschadler, E.
Bueler, D. Holland, J. Johnson, and S. Price, A
Community Ice Sheet Model for Sea Level Prediction: Building a
Next-Generation Community Ice Sheet Model, A Workshop Held at Los
Alamos National Laboratory, Los Alamos, New Mexico, 18-20 August 2008,
Eos, Transactions, Americal Geophysical Union, 90 (3), 23.
- E. Bueler,
Lessons from the short history of ice
sheet model intercomparison, The Cryosphere Discuss.,
2, 399-412, 2008.
- Butcher, E. A., V. Deshmukh, and E.
manifold reduction of periodic delay differential systems,
Proceedings of the ASME 2007 International Design Engineering Technical
Conferences & Computers and Information in Engineering Conference
IDETC/CIE 2007, Las Vegas, Nevada, September 2007.
- Butcher, E. A., P. Nindujarla and E.
up- and down-milling using a Chebyshev collocation method,
Proceedings of ASME IDETC/CIE 2005, Long Beach, CA, September
- Averina, V.,
I. Kolmanovsky, A. Gibson, G. Song and E.
delay-dependent behavior of engine air-to-fuel ratio, Proceedings of the IEEE Conference on
Control Applications, Toronto, August, 2005.
- Butcher, E. A., H. Ma, E. Bueler,
V. Averina, and Z. Szabo, Stability Analysis of Parametrically
Excited Systems with Time-Delay, Proceedings of 19th
Biennial Conference on Mechanical Vibration and Noise, ASME DETC 03,
Chicago, September 2003.
Funded research projects
- Ed Bueler (PI), Mark Fahnestock (Co-I), Andy Aschwanden (Co-I), and
Constantine Khroulev (senior personnel), Understanding
measured variability in the Greenland ice sheet using the Parallel Ice
Sheet Model (PISM), NASA Modeling Analysis and Prediction,
grant #NNX13AM16G, $700K, 2013--2017.
- Ed Bueler (PI), Regine Hock (Co-I), David Maxwell (Co-I), and Martin
Truffer (Co-I), A high resolution
Parallel Ice Sheet Model including fast, sliding flow: advanced
development and application, NASA Modeling Analysis and
Prediction, grant #NNX09AJ38G, $994K, 2009--2013.
- Craig Lingle (PI), Ed Bueler (Co-I) and Dave Covey (Co-I), Ice
Sheet Modeling, A science team component of Polar Radar for Ice Sheet
Measurements (PRISM), NASA Cryospheric Sciences Grant #
NAG5-11371, $436K, 2003--2008.
- Eric A. Butcher (PI) and Ed Bueler (Co-PI), Symbolic Stability and
Bifurcation Analysis of Time-Periodic Differential-Delay Equations:
Applications to High-Speed Machining Models, NSF Award # 0114500,
Division of Civil and Mechanical Systems, $205K, 2001--2004. See separate page on DDEs.
Preprints and Technical Reports
- Ed Bueler and Jed Brown, The
shallow shelf approximation as a "sliding law" in a thermomechanically
coupled ice sheet model, preprint arXiv:0810.3449,
- Ed Bueler, An
exact solution to the temperature equation in a column of ice and
bedrock, preprint arXiv:0710.1314,
- Ed Bueler and Jed Brown, On
exact solutions for cold, shallow, and thermocoupled ice sheets,
- Ed Bueler, Craig S. Lingle, Jed A.
Kallen-Brown, Computation of combined
spherical-elastic and viscous-half-space earth model for ice sheet
simulation, preprint arXiv:physics/0606074,
- Chebyshev collocation for linear,
periodic ordinary and delay differential equations: a posteriori
- Ed Bueler, Craig Lingle, Jed Brown, Dave Covey, and Latrice Bowman, Exact
time-dependent similarity solutions for isothermal shallow ice
sheets, UAF DMS Technical Report 04-01, 2004. (20 pages, 406 KB, PDF)
- Construction of steady state
solutions for isothermal shallow ice sheets, UAF DMS Technical
Report 03-02, 2003. (7 pages, 183 KB, PDF)
- Ed Bueler and Eric Butcher, Stability of periodic linear
delay-differential equations and the Chebyshev approximation of
fundamental solutions. UAF DMS Technical Report 02-03, 2002
(33 pages: PDF).
- Numerical approximation of a two--dimensional thermomechanical
model for ice flow, UAF DMS Technical Report 02-02, 2002. (51
pages, 449 KB, PDF)
- Dirac operators as "annihilation operators" on Riemannian
manifolds, 2001 (8 pages: PDF ).
- Number operators for Riemannian manifolds, arxiv.org/abs/math-ph/0104022,
Computer programs and packages
- with Constantine Khroulev, Andy Aschwanden, Jed Brown, and many
others, PISM, a Parallel Ice Sheet
- I have Matlab codes for
exact solution-based test cases for verifying numerical models of
isothermal and thermomechanically coupled shallow ice sheets.
sheet modeling at UAF page.
- ddec, a Matlab suite for stability
sharts and other information on linear, periodic ODEs and DDEs
Supervised theses and projects by graduate students
- Max Heldman, Toward an optimal solver for the obstacle problem, M.S. Mathematics (project), UAF 2018.
- Lyman Gillispie, A temperature-only formulation for ice sheets, M.S.
Mathematics (thesis), UAF 2014.
- Will Mitchell, Exact
numerical solutions for Stokes flow in glaciers, M.S.
Mathematics (thesis), UAF 2012.
- Daniella DellaGiustina (jointly advised w. M. Truffer), Regional modeling of Greenland’s outlet
glaciers with the Parallel
Ice Sheet Model, M.S. Computational Physics (thesis), UAF
- Jacob Stroh, Non-normality
in scalar delay differential equations, M.S. Mathematics
(thesis), UAF 2006.
- Jed Brown, Multi-modal ice sheet dynamics: theory
and implementation, M.S. Mathematics (project), UAF 2006.
- Tim Carlson, Magnus'
expansion as an approximation tool for ordinary differential
equations, M.S. Mathematics (thesis), UAF 2005.
- Latrice Bowman, Numerical analysis of ice flow, M.S.
Mathematics (project), UAF 2002.
- Victoria Averina, Symbolic stability of delay differential
equations, M.S. Mathematics (thesis), UAF 2002.
- Mikhail Korotiaev, Critical points of the heat kernel on a compact
semisimple Lie group, M.S. Mathematics (thesis), UAF 2002.
- Liane K. Hansen, Numerical solutions to a weighted Hodge
Laplacian on the torus, M.S. Mathematics (project), UAF 1999.
- I am a member of the:
- At one time I wrote reviews for Mathematical
- Mathematical Sciences Research Institute,
Berkeley '97-'98. Postdoctoral Fellow.
- Cornell University, Ithaca '97. Ph.D.
- Cornell University, Ithaca '95. M.S.
- California State University, Chico '91. B.S.