Papers in applied mathematics: numerical ice sheet modeling

• Ed Bueler and Jed Brown (2009). The shallow shelf approximation as a "sliding law" in a thermomechanically coupled ice sheet model, J. Geophys. Res., 114, F03008, doi:10.1029/2008JF001179.
• E. Bueler, J. Brown, and C. Lingle (2007). Exact solutions to the thermomechanically coupled shallow ice approximation: effective tools for verification, J. Glaciol. 53 (182), 499--516.
  
• E. Bueler, C. Lingle, J. Brown (2007). Fast computation of a viscoelastic deformable earth model for ice flow simulations, Ann. Glaciol. 46, 97--105.
• E. Bueler, C. Lingle, J. Kallen-Brown, D. Covey, and L. Bowman (2005). Exact solutions and verification of numerical models for isothermal ice sheets, J. Glaciol. 51 (173), 291--306.
  

Papers in applied mathematics: delay differential equations

• 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.
  

Papers in mathematics

• 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.   And Erratum, one page: PDF , DVI.  Note that a counterexample to the main conjecture was given by G. Carron, Proc. Am. Math. Soc. 2007.  Thus my conjecture should have added the hypothesis "M is topologically tame" (i.e. M is homeomorphic to the interior of a compact manifold).  This is the hypothesis considered in Hodge theory and cohomology with compact supports above.

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. 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.

Funded research projects

• 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, $1.0M, 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.  See ice sheet modeling at UAF page.
  
• 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, 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.

Computer programs and packages

• with Jed Brown, Constantine Khroulev, Andy Aschwanden, and 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

Theses and projects by graduate students

• Jacob Stroh, Non-normality in scalar delay differential equations, M.S. Thesis, UAF 2006.
  
• Jed Brown, Multi-modal ice sheet dynamics: theory and implementation, M.S. Project, UAF 2006.
• Tim Carlson, Magnus' Expansion as an Approximation Tool for Ordinary Differential Equations, M.S. Thesis, UAF 2005.
  
• Latrice Bowman, Numerical Analysis of Ice Flow, M.S. Project, UAF 2002.
  
• Victoria Averina, Symbolic stability of delay differential equations, M.S. Thesis, UAF 2002.
  
• Mikhail Korotiaev, Critical points of the heat kernel on a compact semisimple Lie group, M.S. Thesis, UAF 2002.
  
• Liane K. Hansen, Numerical solutions to a weighted Hodge Laplacian on the torus, M.S. Project, UAF 1999.

Professional activities

• I have written 14 reviews for Mathematical Reviews.
  
• I am a member of the:
• American Mathematical Society
• Society for Industrial and Applied Mathematics

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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.