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.

google scholar citations

- 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

- 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, 4226--4245.
- 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
(3), 031003.

- 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,
2008, 137--149.

- E. Bueler (2007). Error bounds for approximate eigenvalues of periodic-coefficient linear delay differential equations, SIAM J. Num. Analysis 45 (6), 2510--2536.
- E. A. Butcher, H. Ma, E. Bueler,
V. Averina, and Z. Szabo (2004),
*Stability of time-periodic delay-differential equations via Chebyshev polynomials*, Int. J. Numer. Meth. Engng. 59, 895--922.

- E. A. Butcher, H. Ma, and E. Bueler
(2003).
*Chebyshev expansion of linear dynamic systems with time delay and periodic coefficients under control excitations*, J. Dynamic Systems, Measurement and Control (Trans. ASME),**125**, 236--243.

- E. Bueler and I. Prokhorenkov
(2002).
*Hodge theory and cohomology with compact supports*, Soochow J. Math.**28**(1), 33--55. - E. Bueler (1999).
*The heat kernel weighted Hodge Laplacian on noncompact manifolds*, Trans. Am. Math. Soc.**351**(2), 683--713.

Bueler (1999) was my
thesis. See *Erratum* for Theorem 3.4: PDF
, DVI. 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
hypothesis "M is topologically
tame" (i.e. M is homeomorphic to
the interior of a compact manifold with boundary), the hypothesis
considered in Bueler & Prokhorenkov (2002)* *above.

- 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. Bueler, Center 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. Bueler, Stability of up- and down-milling using a Chebyshev collocation method, Proceedings of ASME IDETC/CIE 2005, Long Beach, CA, September 2005.
- Averina, V., I. Kolmanovsky, A. Gibson, G. Song and E. Bueler, Analysis and control of 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.

- 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.

- Ed Bueler and Jed Brown, The shallow shelf approximation as a "sliding law" in a thermomechanically coupled ice sheet model, preprint arXiv:0810.3449, 2008.
- Ed Bueler, An exact solution to the temperature equation in a column of ice and bedrock, preprint arXiv:0710.1314, 2007.
- Ed Bueler and Jed Brown, On exact solutions for cold, shallow, and thermocoupled ice sheets, preprint arXiv:physics/0610106, 2006.
- 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, 2006.
- Chebyshev collocation for linear,
periodic ordinary and delay differential equations: a posteriori
estimates, arxiv.org/abs/math.NA/0409464,
2004

- 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, 2000.

- with Constantine Khroulev, Andy Aschwanden, Jed Brown, and many
others, PISM, a Parallel Ice Sheet
Model

- I have Matlab codes for exact solution-based test cases for verifying numerical models of isothermal and thermomechanically coupled shallow ice sheets. See ice sheet modeling at UAF page.
- ddec, a Matlab suite for stability sharts and other information on linear, periodic ODEs and DDEs

- 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
and
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
2011.

- 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 Reviews*.

Education

- Mathematical Sciences Research Institute, Berkeley '97-'98. Postdoctoral Fellow.
- Cornell University, Ithaca '97. Ph.D. Mathematics
- Cornell University, Ithaca '95. M.S.
Mathematics

- California State University, Chico '91. B.S. Mathematics.

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