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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
<html><head>
<meta content="text/html; charset=ISO-8859-1" http-equiv="content-type">
<meta name="GENERATOR" content="Mozilla/4.76 [en] (Win98; U)
[Netscape]"><title>Ed Bueler's research</title></head><body>
<center>
<h2>Ed Bueler's Research</h2>
</center>
<center> </center>
<center style="color: rgb(0, 0, 0);">My interests include <a href="http://www.pism-docs.org"><span style="font-style: italic;">practical</span> ice sheet models</a>, the
theory of <a href="http://www.gi.alaska.edu/snowice/glaciers/iceflow/">ice
flow</a>,<br>
partial differential equations, variational inequalities, delay
differential equations,<br>
and the numerical analysis thereof.<br>
<br>
<h4>
<a href="cvELB.pdf">current CV</a> (PDF)<br>
<br>
<a href="http://scholar.google.com/citations?user=EwJpBJsAAAAJ&hl=en">google
scholar citations</a> <br>
</h4>
<br>
</center>
<h4>Papers in applied mathematics: numerical ice sheet modeling<br>
</h4>
See my <a href="cvELB.pdf">current CV</a> (PDF) for this still-growing set of papers.<br>
<h4> </h4>
<h4>Papers in applied mathematics: delay differential equations and their
numerical analysis<br>
</h4>
<ul>
<li>E. A. Butcher, M. Sari, <span style="font-weight: bold;">E. Bueler</span>,
and T. Carlson (2009). <a href="http://dx.doi.org/10.1016/j.cnsns.2009.02.030"><span style="font-style: italic;">Magnus' expansion for time-periodic
systems: parameter-dependent approximations</span></a>, Commun.
Nonlinear Sci. Numer. Simulat. <span style="font-weight: bold;">14</span>,
4226--4245<span class="pubTitle" style="margin: 0px;"></span>. </li>
<li>E. A. Butcher, O. A. Bobrenkov, <span style="font-weight: bold;">E.
Bueler</span>, and P. Nindujarla (2009). <a style="font-style: italic;" href="papers/CND-08-1016.pdf">Analysis of milling stability by the
Chebyshev collocation method: Algorithm and optimal stable immersion
levels</a>, J. Comput. Nonlinear Dynam. <span style="font-weight: bold;">4</span>
(3), 031003.<br>
</li>
<li> V. Deshmukh, E.A. Butcher, and <span style="font-weight: bold;">E.
Bueler</span> (2008). <a href="http://www.springerlink.com/content/np085r68831r5782/"><span style="font-style: italic;">Dimensional reduction of nonlinear delay
differential equations with periodic coefficients using Chebyshev
spectral collocation</span></a>, Nonlinear Dynamics <span style="font-weight: bold;">52</span>,
2008, 137--149.<br>
</li>
<li><span style="font-weight: bold;">E. Bueler</span> (2007). <a href="http://link.aip.org/link/?SNA/45/2510"><span style="font-style: italic;">Error bounds for approximate eigenvalues
of periodic-coefficient linear delay differential equations</span></a>,
SIAM J. Num. Analysis<span style="color: rgb(0, 0, 0);"> </span><font style="color: rgb(0, 0, 0);" color="#333399"> <span style="font-weight: bold;">45</span> (6),
2510--2536.</font> </li>
<li>E. A. Butcher, H. Ma, <span style="font-weight: bold;">E. Bueler</span>,
V. Averina, and Z. Szabo (2004), <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.114.9772&rep=rep1&type=pdf"><i>Stability
of
time-periodic
delay-differential
equations via Chebyshev polynomials</i></a>, Int. J. Numer.
Meth. Engng. <span style="font-weight: bold;">59</span>, 895--922.<br>
</li>
<li>E. A. Butcher, H. Ma, and <span style="font-weight: bold;">E. Bueler</span>
(2003). <a href="http://link.aip.org/link/?JDSMAA/125/236/1"><i>Chebyshev
expansion
of linear dynamic systems with time delay and periodic coefficients
under control excitations</i></a>, J. Dynamic Systems, Measurement
and Control (Trans. ASME), <b>125</b>, 236--243.<br>
</li>
</ul>
<h4> </h4>
<h4>Papers in mathematics</h4>
<ul>
<li><span style="font-weight: bold;">E. Bueler</span> and I. Prokhorenkov
(2002). <a href="http://arxiv.org/abs/math/9804152"><i>Hodge theory and
cohomology with compact supports</i></a>, Soochow J. Math. <b>28</b>
(1), 33--55.</li>
<li><span style="font-weight: bold;">E. Bueler</span> (1999). <a href="http://www.ams.org/tran/1999-351-02/S0002-9947-99-02021-8/S0002-9947-99-02021-8.pdf"><i>The
heat
kernel
weighted
Hodge Laplacian on noncompact manifolds</i></a>, Trans. Am. Math.
Soc. <b>351</b> (2), 683--713.</li>
</ul>
<div style="text-align: left; margin-left: 80px;">Bueler (1999) was my
thesis. See <i>Erratum</i> for Theorem 3.4: <a href="papers/errtams.pdf">PDF</a>
, <a href="papers/errtams.dvi">DVI</a>. Confirmation of conjecture
6.3, the second of three in the paper, appears in <a href="http://dx.doi.org/10.1093/qjmath/52.2.171">Gong
& Wang (2001), Quart. J. Math</a>. A counterexample to my
conjecture 1.1 was given by <a href="http://dx.doi.org/10.1090/S0002-9939-07-08713-8">G.
Carron (2007), Proc. AMS</a>. Conjecture 1.1 should have added the
hypothesis "<span style="font-style: italic;">M</span> is topologically
tame" (i.e. <span style="font-style: italic;">M</span> is homeomorphic to
the interior of a compact manifold with boundary), the hypothesis
considered in Bueler & Prokhorenkov (2002)<span style="text-decoration: underline;"><span style="font-style: italic;"></span></span><i> </i>above. </div>
<h4> </h4>
<h4>Reviewed conference proceedings, commentaries, and short notes<br>
</h4>
<ul>
<li>W. Lipscomb, R. Bindschadler, <span style="font-weight: bold;">E.
Bueler</span>, D. Holland, J. Johnson, and S. Price, <span style="font-style: italic;">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</span>,
Eos, Transactions, Americal Geophysical Union, 90 (3), 23.<br>
</li>
<li><span class="pb_toc_link"><span style="font-weight: bold;">E. Bueler</span>,
<a href="http://www.the-cryosphere-discuss.net/2/399/2008/tcd-2-399-2008.html"><span style="font-style: italic;">Lessons from the short history of ice
sheet model intercomparison</span></a>, The Cryosphere Discuss.,
2, 399-412, 2008.</span></li>
<li>Butcher, E. A., V. Deshmukh, and <span style="font-weight: bold;">E.
Bueler</span>, <span style="font-style: italic;"><a href="papers/ButcheretalProceedDETC07.pdf">Center
manifold reduction of periodic delay differential systems</a>,</span>
Proceedings of the ASME 2007 International Design Engineering Technical
Conferences & Computers and Information in Engineering Conference
IDETC/CIE 2007, Las Vegas, Nevada, September 2007.</li>
<li>Butcher, E. A., P. Nindujarla and <span style="font-weight: bold;">E.
Bueler</span>, <a href="papers/longbeachpaperfinal.pdf"><span style="font-style: italic;">Stability
of
up- and down-milling using a Chebyshev collocation method</span></a>,
Proceedings of ASME IDETC/CIE 2005, Long Beach, CA, September
2005.<font color="#333399"><font color="#333399"> </font></font></li>
<li><font color="#333399"><span style="color: rgb(0, 0, 0);">Averina, V.,
I. Kolmanovsky, A. Gibson, G. Song and <span style="font-weight: bold;">E.
Bueler</span>, </span><span style="font-style: italic; color: rgb(0, 0, 0);"><a href="http://ieeexplore.ieee.org/iel5/10069/32294/01507298.pdf?tp=&isnumber=&arnumber=1507298">Analysis
and
control
of
delay-dependent behavior of engine air-to-fuel ratio</a>, </span><span style="color: rgb(0, 0, 0);">Proceedings of the IEEE Conference on
Control Applications, Toronto, August, 2005.</span></font></li>
<li>Butcher, E. A., H. Ma, <span style="font-weight: bold;">E. Bueler</span>,
V. Averina, and Z. Szabo, <i>Stability Analysis of Parametrically
Excited Systems with Time-Delay</i>, Proceedings of 19th
Biennial Conference on Mechanical Vibration and Noise, ASME DETC 03,
Chicago, September 2003.</li>
</ul>
<h4>Funded research projects</h4>
<ul>
<li>Ed Bueler (PI), Mark Fahnestock (Co-I), Andy Aschwanden (Co-I), and
Constantine Khroulev (senior personnel), <span style="font-style: italic;">Understanding
measured variability in the Greenland ice sheet using the Parallel Ice
Sheet Model (PISM)</span>, NASA Modeling Analysis and Prediction,
grant #NNX13AM16G, $700K, 2013--2017. </li>
<li>Ed Bueler (PI), Regine Hock (Co-I), David Maxwell (Co-I), and Martin
Truffer (Co-I), <span style="font-style: italic;">A high resolution
Parallel Ice Sheet Model including fast, sliding flow: advanced
development and application</span>, NASA Modeling Analysis and
Prediction, grant #NNX09AJ38G, $994K, 2009--2013. </li>
<li>Craig Lingle (PI), Ed Bueler (Co-I) and Dave Covey (Co-I), <i>Ice
Sheet Modeling, A science team component of Polar Radar for Ice Sheet
Measurements (PRISM)</i>, NASA Cryospheric Sciences Grant #
NAG5-11371, $436K, 2003--2008.<br>
</li>
<li>Eric A. Butcher (PI) and Ed Bueler (Co-PI), <i>Symbolic Stability and
Bifurcation Analysis of Time-Periodic Differential-Delay Equations:
Applications to High-Speed Machining Models</i>, NSF Award # 0114500,
Division of Civil and Mechanical Systems, $205K, 2001--2004. See <a href="ddes/ddepage.htm">separate page on DDEs</a>. </li>
</ul>
<h4>Preprints and Technical Reports<br>
</h4>
<ul>
<span style="color: rgb(51, 51, 153);"></span>
<li>Ed Bueler and Jed Brown, <span style="font-style: italic;">The
shallow shelf approximation as a "sliding law" in a thermomechanically
coupled ice sheet model</span>, preprint <a href="http://arxiv.org/abs/0810.3449">arXiv:0810.3449</a>,
2008.</li>
<li style="color: rgb(0, 0, 0);">Ed Bueler, <span style="font-style: italic;">An
exact solution to the temperature equation in a column of ice and
bedrock</span>, preprint <a href="http://arxiv.org/abs/0710.1314">arXiv:0710.1314</a>,
2007.</li>
<li style="color: rgb(0, 0, 0);">Ed Bueler and Jed Brown, <span style="font-style: italic;">On
exact solutions for cold, shallow, and thermocoupled ice sheets</span>,
preprint <a href="http://arxiv.org/abs/physics/0610106">arXiv:physics/0610106</a>,
2006.</li>
<li style="color: rgb(0, 0, 0);">Ed Bueler, Craig S. Lingle, Jed A.
Kallen-Brown, <span style="font-style: italic;">Computation of combined
spherical-elastic and viscous-half-space earth model for ice sheet
simulation</span>, preprint <a href="http://arxiv.org/abs/physics/0606074">arXiv:physics/0606074</a>,
2006.</li>
<li><span style="font-style: italic;">Chebyshev collocation for linear,
periodic ordinary and delay differential equations: a posteriori
estimates</span>, <a href="http://arxiv.org/abs/math.NA/0409464">arxiv.org/abs/math.NA/0409464</a>,
2004<br>
</li>
<li>Ed Bueler, Craig Lingle, Jed Brown, Dave Covey, and Latrice Bowman, <i>Exact
time-dependent similarity solutions for isothermal shallow ice
sheets</i>, UAF DMS Technical Report 04-01, 2004. (20 pages, 406 KB, <a href="papers/simice.pdf">PDF</a>)</li>
<li><span style="font-style: italic;">Construction of steady state
solutions for isothermal shallow ice sheets</span>, UAF DMS Technical
Report 03-02, 2003. (7 pages, 183 KB, <a href="papers/steadyiso.pdf">PDF</a>)</li>
<li>Ed Bueler and Eric Butcher, <i>Stability of periodic linear
delay-differential equations and the Chebyshev approximation of
fundamental solutions.</i> UAF DMS Technical Report 02-03, 2002
(33 pages: <a href="papers/dde.pdf">PDF</a>).</li>
<li><i>Numerical approximation of a two--dimensional thermomechanical
model for ice flow</i>, UAF DMS Technical Report 02-02, 2002. (51
pages, 449 KB, <a href="papers/twoDtemp.pdf">PDF</a>) </li>
<li><i>Dirac operators as "annihilation operators" on Riemannian
manifolds,</i> 2001 (8 pages: <a href="papers/doao.pdf">PDF</a> ).</li>
<li> <i>Number operators for Riemannian manifolds,</i> <a href="http://arxiv.org/abs/math-ph/0104022">arxiv.org/abs/math-ph/0104022</a>,
2000.</li>
</ul>
<h4>Computer programs and packages</h4>
<ul>
<li>with Constantine Khroulev, Andy Aschwanden, Jed Brown, and many
others, <a href="http://www.pism-docs.org">PISM, a Parallel Ice Sheet
Model</a><br>
</li>
<li>I have <span style="font-style: italic;">Matlab </span>codes for
exact solution-based test cases for verifying numerical models of
isothermal and thermomechanically coupled shallow ice sheets.
See <a href="http://www.gi.alaska.edu/snowice/glaciers/iceflow">ice
sheet modeling at UAF</a> page. </li>
<li> <a href="ddes/DDEcharts.htm">ddec</a>, a Matlab suite for stability
sharts and other information on linear, periodic ODEs and DDEs </li>
</ul>
<h4>Theses by graduate students I have supervised<br>
</h4>
<ul>
<li>Lyman Gillispie, <span style="font-style: italic;"><a href="papers/lgillispieMS.pdf">A temperature-only formulation for ice sheets</a>,</span> M.S.
Mathematics (thesis), UAF 2014.</li>
<li>Will Mitchell, <span style="font-style: italic;"><a href="http://www.math.wisc.edu/%7Ewhmitchell/WM_2012_MSTHESIS.pdf">Exact
and
numerical solutions for Stokes flow in glaciers</a>,</span> M.S.
Mathematics (thesis), UAF 2012.<br>
</li>
<li>Daniella DellaGiustina (jointly advised w. M. Truffer), <a href="http://www2.gi.alaska.edu/snowice/glaciers/iceflow/ddellagiustinaMS.pdf"><span style="font-style: italic;">Regional modeling of Greenland’s outlet
glaciers with the</span><span style="font-style: italic;"> Parallel
Ice Sheet Model</span></a>, M.S. Computational Physics (thesis), UAF
2011.<br>
</li>
<li>Jacob Stroh, <a href="papers/jnstrohMS.pdf"><span style="font-style: italic;">Non-normality
in scalar delay differential equations</span></a>, M.S. Mathematics
(thesis), UAF 2006.<br>
</li>
<li>Jed Brown, <a href="http://www2.gi.alaska.edu/snowice/glaciers/iceflow/slidesJBrown.pdf"><span style="font-style: italic;">Multi-modal ice sheet dynamics: theory
and implementation</span></a>, M.S. Mathematics (project), UAF 2006.</li>
<li>Tim Carlson, <a href="papers/tcarlsonMS.pdf"><span style="font-style: italic;">Magnus'
expansion as an approximation tool for ordinary differential
equations</span></a>, M.S. Mathematics (thesis), UAF 2005.<br>
</li>
<li>Latrice Bowman, <i>Numerical analysis of ice flow</i>, M.S.
Mathematics (project), UAF 2002.<br>
</li>
<li>Victoria Averina, <i>Symbolic stability of delay differential
equations</i>, M.S. Mathematics (thesis), UAF 2002.<br>
</li>
<li>Mikhail Korotiaev, <i>Critical points of the heat kernel on a compact
semisimple Lie group</i>, M.S. Mathematics (thesis), UAF 2002.<br>
</li>
<li> Liane K. Hansen, <i>Numerical solutions to a weighted Hodge
Laplacian on the torus</i>, M.S. Mathematics (project), UAF 1999.</li>
</ul>
<h4>Professional activities</h4>
<ul>
<li> I am a member of the:</li>
<ul>
<li> <a href="http://www.siam.org">Society for Industrial and Applied
Mathematics</a></li>
<li><a href="http://www.igsoc.org">International Glaciological Society</a></li>
</ul>
<li>At one time I wrote <a href="reviewspage.htm">reviews</a> for <i>Mathematical
Reviews</i>.<br></li>
</ul>
<h4>
<hr width="100%">Education</h4>
<ul>
<li> Mathematical Sciences Research Institute,
Berkeley '97-'98. Postdoctoral Fellow.</li>
<li> Cornell University, Ithaca '97. Ph.D.
Mathematics</li>
<li> Cornell University, Ithaca '95. M.S.
Mathematics<br>
</li>
<li> California State University, Chico '91. B.S.
Mathematics.</li>
</ul>
<hr width="100%"><a href="http://www.cs.uaf.edu/cgi-bin/doc-info.prl">doc
info</a><br>
<br>
</body></html>