Andrew Gillette
Research
Research
CV
Click here to download my Curriculum Vitae (updated Feb 2013).
Research Interests
Employment and Education
Assistant Professor of Mathematics, University of Arizona (starting in fall 2013)
Postdoc in Mathematics, UC San Diego (2011-)
advised by Dr. Michael Holst
with support from the National Biomedical Computation Resource
Ph.D. in Mathematics, UT Austin (2011)
advised by Dr. Chandrajit Bajaj
B.A. in Mathematics, Amherst College (2004)
advised by Dr. Rob Benedetto
Publications
In addition to the list below, I maintain sites through arXiv.org and Google Scholar citations.
*** Click on a column header to re-sort the table. ***
| Count | Year | Authors | Title | Topic | Status |
|---|---|---|---|---|---|
| 17 | 2013 | M. Floater, A. Gillette, N. Sukumar |
Gradient Bounds for Wachspress Coordinates on Polytopes
Submitted [pdf] |
finite element analysis | submitted | 16 | 2013 | P. Kekenes-Huskey, T. Liao, A. Gillette, J. Hake, Y. Zhang, A. Michailova, A.D. McCulloch, J.A. McCammon | Molecular and Sub Cellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice
Submitted [bib] |
computational molecular biology | submitted |
| 15 | 2012 | A. Gillette | Hermite and Bernstein Style Basis Functions for Cubic Serendipity Spaces on Squares and Cubes
Submitted [bib] [pdf] [arxiv] [slides] |
finite element analysis | submitted | 14 | 2012 | P. Kekenes-Huskey, A. Gillette, J. Hake, J.A. McCammon | Finite Element Estimation of Protein-Ligand Association Rates with Post-Encounter Effects: Applications to Calcium binding in Troponin C and SERCA
Computational Science and Discovery [bib] [doi] |
computational molecular biology | journal article | 13 | 2012 | A. Gillette, M. Holst | Finite Element Exterior Calculus for Evolution Problems
Submitted [bib] [pdf] [arxiv] [slides] |
finite element analysis | submitted | 12 | 2011 | A. Rand, A. Gillette, C. Bajaj | Interpolation Error Estimates for Mean Value Coordinates
Advances in Computational Mathematics [bib] [pdf] [doi] [arxiv] |
finite element analysis | journal article | 11 | 2011 | A. Rand, A. Gillette, C. Bajaj | Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
Mathematics of Computation [bib] [pdf] [arxiv] |
finite element analysis | journal article | 10 | 2011 | A. Gillette | Stability of Dual Discretization Methods for Partial Differential Equations
PhD Dissertation, UT Austin [bib] [pdf] [doi] |
finite element analysis | dissertation | 9 | 2011 | A. Gillette, C. Bajaj | Dual Formulations of Mixed Finite Element Methods with Applications
Computer Aided Design [bib] [pdf] [doi] |
discrete exterior calculus | journal article | 8 | 2010 | A. Gillette, A. Rand, C. Bajaj | Error Estimates for Generalized Barycentric Interpolation
Advances in Computational Mathematics [bib] [pdf] [doi] [arxiv] [poster] |
finite element analysis | journal article | 7 | 2010 | A. Gillette, C. Bajaj | A Generalization for Stable Mixed Finite Elements
Proc. ACM Symposium on Solid and Physical Modeling [bib] [pdf] [doi] [slides] * Winner of Best Paper Award * |
discrete exterior calculus | proceedings | 6 | 2009 | A. Gillette | Notes on Discrete Exterior Calculus
Technical Report, UT Austin [bib] [pdf] |
discrete exterior calculus | technical report | 5 | 2009 | C. Bajaj, A. Gillette, Q. Zhang | Stable Mesh Decimation
Proc. SIAM-ACM Conf. on Geom. and Phys. Modeling [bib] [pdf] [doi] [poster] |
computational geometry / topology | proceedings | 4 | 2009 | C. Bajaj, A. Gillette, S. Goswami, B. Kwon, J. Rivera | Complementary Space for Enhanced Uncertainty and Dynamics Visualization
Topological Methods in Data Analysis and Visualization [bib] [pdf] [doi] |
computational geometry / topology | book chapter | 3 | 2008 | C. Bajaj, A. Gillette | Quality Meshing of a Forest of Branching Structures
Proc. 17th Intl. Meshing Roundtable [bib] [pdf] [doi] [slides] |
computational geometry / topology | proceedings | 2 | 2007 | S. Goswami, A. Gillette, C. Bajaj | Efficient Delaunay Mesh Generation From Sampled Scalar Functions
Proc. 16th Intl. Meshing Roundtable [bib] [pdf] [doi] [slides] |
computational geometry / topology | proceedings | 1 | 2007 | C. Bajaj, A. Gillette, S. Goswami | Topology Based Selection and Curation of Level Sets
Topology-Based Methods in Visualization [bib] [pdf] [doi] [slides] |
computational geometry / topology | book chapter |
Talks
*** Click on a column header to re-sort the table. ***
| Date | Title | Topic | Forum | Location |
|---|---|---|---|---|
| May 2013 | Analysis and Application of Polygonal and Serendipity Finite Element Methods | barycentric coordinates / serendipity elements | invited seminar | University of Oslo, Norway |
| May 2013 | Serendipity Finite Element Methods for Cardiac Electrophysiology Models | serendipity elements | Workshop on Advancing Numerical Technologies in the Cardiac Domain | Simula Research Laboratory, Oslo, Norway |
| Apr 2013 | Basis Functions for Serendipity Finite Element Methods | serendipity elements | 14th International Conference on Approximation Theory | San Antonio, TX |
| Mar 2013 | An Introduction to Hermite Serendipity Finite Element Methods | serendipity elements | invited colloquium | Cal Poly Pomona |
| Feb 2013 | Cubic Serendipity Basis Functions for Isogeometric Analysis | serendipity elements | Advances in Computational Mechanics / Tom Hughes' 70th Birthday | San Diego, CA |
| Feb 2013 | Analysis and Applications of Polygonal and Serendipity Finite Element Methods | barycentric coordinates / serendipity elements | invited colloquium | Southern Methodist University |
| Feb 2013 | Hermite Polynomials and Geometric Decompositions | serendipity elements | invited undergraduate seminar | Loyola Marimount University |
| Feb 2013 | Analysis and Applications of Polygonal and Serendipity Finite Element Methods | barycentric coordinates / serendipity elements | invited colloquium | University of Arizona |
| Jan 2013 | Geometric Decomposition of Serendipity Finite Element Spaces | serendipity elements | AMS-MAA Joint Meetings | San Diego, CA |
| Oct 2012 | Fewer Degrees of Freedom, Same Convergence Rate: Recent progress in serendipity finite element methods | serendipity elements | invited seminar | Georgia Tech |
| Aug 2012 | Using FEniCS for Finite Element Methods | finite element software | tutorial at National Biomedical Computation Resource Summer Institute | UC San Diego |
| Jul 2012 | Error Estimates for Generalized Barycentric Coordinate Finite Element Methods | barycentric coordinates | plenary lecture at NSF Workshop on Barycentric Coordinates | Columbia University |
| Jul 2012 | The Geometry of Interpolation Error Estimates for Isogeometric Analysis
[** audio from SIAM **] |
isogeometric analysis | SIAM Annual Meeting | Minneapolis, MN |
| Dec 2011 | Finite Element Exterior Calclus for Evolution Problems | finite element analysis | ICES / CVC Seminar | UT Austin |
| Nov 2011 |
Finite Element Clifford Algebra: A New Toolkit for Evolution Problems
[** audio from SIAM **] | finite element analysis | SIAM Conference on Analysis of PDEs | San Diego, CA |
| Nov 2011 | Discrete Exterior Calculus and Polygonal Finite Elements | discrete exterior calculus | Workshop on Geometric Numerical Methods for PDEs | UC San Diego |
| Oct 2011 | Geometric Criteria for Generalized Barycentric Finite Elements | barycentric coordinates | SIAM-ACM Joint Conference on Geometric and Physical Modeling | Orlando, FL |
| Oct 2011 | Generalized Barycentric Coordinates for Polygonal Finite Elements | barycentric coordinates | CCOM Seminar | UC San Diego |
| May 2011 | Stability of Dual Discretization Methods for Partial Differential Equations | finite element analysis | thesis defense | UT Austin |
| Feb 2011 | Modeling Electrical Activity in Neurons with Discrete Calculus | biological modeling | undergraduate math club | UT Austin |
| Jan 2011 | Conforming Vector Interpolation Functions for Polyhedral Meshes | discrete exterior calculus | invited seminar | Los Alamos National Laboratory, NM |
| Jan 2011 | Dual Interpolants for Finite Element Methods | finite element analysis | AMS-MAA Joint Meetings | New Orleans, LA |
| Nov 2010 | Compatibility Conditions for Dual Discretization Methods | discrete exterior calculus | CVC Group Meeting | UT Austin |
| Sep 2010 | A Generalization for Stable Mixed Finite Elements | discrete exterior calculus | ACM Symposium on Solid and Physical Modeling | Haifa, Israel |
| Jun 2010 | Real Algebraic Finite Elements and deRham Cohomology | discrete exterior calculus | invited seminar | KAUST, Saudi Arabia |
| Apr 2010 | DEC-deRham Conformity for Mixed Finite Element Methods | discrete exterior calculus | Demkowicz Group Meeting | UT Austin |
| Apr 2010 | Voronoi Diagrams: Fencing Out Your Neighbors | Voronoi diagrams | Sunday Math Circle | UT Austin |
| Apr 2010 | Cohomology Stability Criteria for Mixed Finite Element Methods | discrete exterior calculus | TACG Seminar | UT Austin |
| Mar 2010 | New Model Stability Criteria for Mixed Finite Elements | discrete exterior calculus | CVC Group Meeting | UT Austin |
| Oct 2009 | Multi-scale Modeling of Electric Activity of Spiny Dendrites in the Hippocampus | biological modeling | AMS Fall Central Section Meeting | Baylor University |
| Jun 2009 | Automated Neuronal Reconstruction: Current Challenges and Proposed Quantification | biolgoical modeling | CVC Group Meeting | UT Austin |
| Feb 2009 | Geometric Discretization of Stress and Elasticity | discrete exterior calculus | CVC Group Meeting | UT Austin |
| Jan 2009 | Applications of the Hodge Decomposition to Biological Structure and Function Modeling | biological modeling | AMS-MAA Joint Meetings | Washington, DC |
| Dec 2008 | Applications of the Hodge Decomposition to Biological Structure and Function Modeling | biological modeling | candidacy exam | UT Austin |
| Oct 2008 | Quality Meshing of a Forest of Branching Structures | biological modeling | 17th International Meshing Roundtable | Pittsburgh, PA |
| Sep 2008 | Discrete Mathematics for Molecular Models | biological modeling | undergraduate math club | UT Austin |
| Aug 2008 | Topology-controlled Stable Function Modeling for Biology | biological modeling | CVC Group Meeting | UT Austin |
| Apr 2008 | Persistent Homology: A Tool For Molecular Modeling | biological modeling | Junior Topology Seminar | UT Austin |
| Jan 2008 | The State of Affairs in Protein Modeling | biological modeling | CVC Group Meeting | UT Austin |
| Nov 2007 | Critical Problems with Critical Points | computational geometry / topology | CVC Group Meeting | UT Austin |
| Oct 2007 | Efficient Delaunay Mesh Generation From Sampled Scalar Functions | computational geometry / topology | 16th International Meshing Roundtable | Seattle, WA |
| Mar 2007 | Topology Based Selection and Curation of Level Sets | computational geometry / topology | Topology In Visualization conference | Grimma, Germany |
| Feb 2007 | An Unstable Instance of the Finite Element Method | finite element analysis | CVC Group Meeting | UT Austin |
Posters
Exterior Calculus for Generalized Barycentric Interpolation
A. Gillette, A. Rand, C. Bajaj
NSF-CBMS Conference: Finite Element Exterior Calculus, 2012.
[pdf]
Error Estimates for Generalized Barycentric Interpolation
A. Gillette, A. Rand, C. Bajaj
IMA Workshop: Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques, 2010.
[pdf]
Electrophysiological Models Derived from EM Reconstructions
J. Edwards, A. Gillette, R. K. Bettadapura, A. Rand, C. Rumsey, Q. Zhang, D. Johnston, K. Harris, C. Bajaj
The National Academies Keck Futures Initiative Conference on Imaging Science, 2010.
[pdf]
Stable Mesh Decimation
C. Bajaj, A. Gillette, Q. Zhang
SIAM-ACM Joint Conference on Geometric and Physical Modeling, 2009.
[pdf]
Spatially Realistic and Reduced Electrophysiology Models Dervied From EM Reconstruction
A. Gillette, R. Bettadapura, F. Chowdhury, J. Edwards, A. Gopinath, J. Rivera, B. Subramanian, A. Rand, C. Rumsey, Q. Zhang, D. Johnston, K. Harris, C. Bajaj, T. Bartol, D. Keller, J. Kinney, T. Sejnowski
MPG-HHMI Janelia Farm High-Resolution Circuit Reconstruction Conference, 2009.
[pdf]
14th International Conference on Approxmation Theory, San Antonio, TX, April 2013.
Advances in Computational Mechanics - Celebrating the 70th Birthday of Thomas J.R. Hughes, San Diego, CA, February 2013.
Workshop on Geometric Numerical Methods for PDE: FEEC + AFEM @ UCSD , San Diego, CA, January 2013.
AMS-MAA Joint Mathematics Meetings, San Diego, CA, January 2013.
(Organizer for AMS Special Session on Finite Element Exterior Calculus and Applications )
Cardiac Physiome Workshop, San Diego, CA, October 2012.
SIAM Conference on the Life Sciences, San Diego, CA, August 2012.
(Organizer for session on Computational Biological Modeling at the Interface of Molecular Simulation and Continuum Diffusion)
National Biomedical Computation Resource Summer Institute (Instructor), UC San Diego, August 2012.
NSF Workshop on Barycentric Coordinates in Geometry Processing and Finite/Boundary Element Methods, New York, NY, July 2012.
SIAM Annual Meeting, Minneapolis, MN, July 2012.
NSF-CBMS Conference: Finite Element Exterior Calculus, ICERM, Providence, RI, June 2012.
SIAM Conference on Analysis of Partial Differential Equations, San Diego, CA, November 2011.
Workshop on Geometric Numerical Methods for PDE, San Diego, CA, November 2011.
SIAM-ACM Joint Conference on Geometric and Physical Modeling, Orlando, FL, October 2011.
Finite Element Rodeo 2011, College Station, TX, February 2011.
Isogeometric Analysis 2011: Integrating Design and Analysis, Austin, TX, January 2011.
AMS-MAA Joint Mathematics Meetings, New Orleans, LA, January 2011.
IMA Workshop: Numerical Solutions of Partial Differential Equations: Novel Discretization Techniques, Minneapolis, MN, November 2010.
ACM Symposium on Solid and Physical Modeling, Haifa, Israel, September 2010.
Algorithms in MacroMolecular Modeling Conference, Austin, TX, November 2009.
AMS Fall Central Section Meeting, Waco, TX, October 2009.
SIAM-ACM Joint Conference on Geometric and Physical Modeling, San Francisco, CA, October 2009.
Summer School Workshop on Multivariate Splines and Their Applications, Athens, GA, May 2009.
Mathematical Aspects of Imaging, Modelling and Visualization in Multiscale Biology, Austin, TX, March 2009. (Organizer)
AMS-MAA Joint Mathematics Meetings, Washington, DC, January 2009.
(Organizer and speaker for AMS Special Session on Mathematical Models of Biological Structures and Function)
17th International Meshing Roundtable, Pittsburgh, PA, October 2008.
IMA Tutorial: Mathematics of Proteins, Minneapolis, MN, January 2008.
16th International Meshing Roundtable, Seattle, WA, October 2007.
Topology in Visualization, Grimma, Germany, March 2007.
AMS-MAA Joint Mathematics Meetings, San Antonio, TX, January 2006.
Conferences and Workshops