John Burkardt
Publications

Jeff Borggaard, John Burkardt, John Burns, Eugene Cliff,
Max Gunzburger, Hongchul Kim, HyungChun Lee, Janet Peterson,
Ajit Shenoy, X Wu,
Algorithms for flow control and optimization,
in Optimal Design and Control:
Proceedings of the Workshop on Optimal Design and Control,
Blacksburg, Virginia, April 89, 1994,
Birkhaeuser, Boston 1995,
ISBN: 0817638083,
LC: TJ212W675.

John Burkardt,
Sensitivity analyses and computational shape optimization for
incompressible flows,
PhD Thesis, Virginia Polytechnic Institute and State University,
ProQuest LLC, Ann Arbor, MI, 1995,
thesis_1995.pdf.

John Burkardt, Qiang Du, Max Gunzburger, HyungChun Lee,
Reducedorder modeling of complex systems,
Proceedings, NA03 Dundee 2003,
bdgl_2003.pdf.

John Burkardt, Max Gunzburger,
Sensitivity discrepancy for geometric parameters,
Proceedings, AIAA Conference, 1995,
sanfran_1995.pdf.

John Burkardt, Max Gunzburger, HyungChun Lee,
Centroidal Voronoi tessellationbased reducedorder modeling
of complex systems,
SIAM Journal on Scientific Computing,
Volume 28, Number 2, 2006, pages 459484,
MR2231716.pdf.

John Burkardt, Max Gunzburger, HyungChun Lee,
POD and CVTbased reducedorder modeling of NavierStokes flows,
Computer Methods in Applied Mechanics and Engineering,
Volume 196, Number 13, 1 December 2006, pages 337355,
MR2270135.pdf.

John Burkardt, Max Gunzburger, Janet Peterson,
Insensitive functionals, inconsistent gradients, spurious minima,
and regularized functionals in flow optimization problems,
International Journal of Computational Fluid Dynamics,
Volume 16, Number 3, 2002, pages 171185,
MR1905748.pdf.

John Burkardt, Max Gunzburger, Janet Peterson,
Discretization of cost and sensitivities in shape optimization,
in Computation and Control IV,
edited by Bowers and Lund,
Proceedings of the Fourth Bozeman Conference on Computation
and Control,
Birkhaeuser, 1995,
MR1349582.pdf.

John Burkardt, Max Gunzburger, Janet Peterson,
Rebecca Brannon,
User manual and supporting information for library of codes
for centroidal Voronoi point placement and associated zeroth,
first and second moment determination,
Technical Report: SAND20020099,
Sandia National Laboratories, February 2002,
bgpb_2002.pdf.

John Burkardt, Max Gunzburger, Clayton Webster,
Reduced order modeling of some nonlinear stochastic
partial differential equations,
International Journal of Numerical Analysis and Modeling,
Volume 4, Number 34, 2007, pages 368391,
MR2344047.pdf.

John Burkardt, Max Gunzburger, Wenju Zhao,
Highprecision computations of the weak Galerkin methods
for the fourthorder problem,
Numerical Algorithms, Volume 84, 2020,
MR4089696.pdf.

John Burkardt, Charles Hall, Thomas Porsching,
The dual variable method for the solution of compressible
fluid flow problems,
SIAM Journal on Algebraic and Discrete Methods,
Volume 7, Number 3, July 1986, pages 476483,
bhp_1986.pdf.

John Burkardt, Wenlong Pei, Catalin Trenchea,
A stress test for the midpoint timestepping method,
International Journal of Numerical Analysis and Modeling,
Accepted.

John Burkardt, Janet Peterson,
Control of steady incompressible 2D channel flow,
in Flow Control,
edited by Max Gunzburger,
Proceedings of IMA Period of Concentration on Flow Control,
The IMA Volumes in Mathematics and Its Applications,
Volume 68, pages 111126,
Springer, 1995,
ISBN: 0387944451,
LC: TA357.F538,
MR1348644.pdf.

John Burkardt, Yixuan Wu, Yanzhi Zhang,
A unified meshfree pseudospectral method for solving both classical and
fractional PDEs,
SIAM Journal on Scientific Computing,
Volume 43, Number 2, 2021, pages A1389A1411.
bwz_2021.pdf.

James Cavendish, Michael Wenner, John Burkardt, Charles Hall,
Thomas Porsching,
DEM: A new computational approach to sheet metal forming,
International Journal for Numerical Methods in
Mechanical Engineering,
Volume 23, Number 5, May 1986, pages 847862.

James Cavendish, Michael Wenner, John Burkardt, Charles Hall,
A new approach to sheet metal forming problems,
Numerical Methods in Industrial Forming Processes,
Numiform 86, 1986, pages 315320,
ISBN13: 9789061916598

James Cavendish, Michael Wenner, John Burkardt, Charles Hall,
Werner Rheinboldt,
Punch stretching of sheet metal and differential equations on manifolds,
International Journal for Numerical Methods in Engineering,
Volume 25, Number 1, January, 1988, pages 269282,
cwbhr_1988.pdf.

Michael Eldred, John Burkardt,
Comparison of nonintrusive polynomial chaos and stochastic
collocation methods for uncertainty quantification,
American Institute of Aeronautics and Astronautics,
Paper 20090976,
47th AIAA Aerospace Sciences Meeting Including The New Horizons
Forum and Aerospace Exposition,
5  8 January 2009, Orlando, Florida,
eb_aiaa_asm_2009.pdf.

Nobuyuki Fukawa, Yanzhi Zhang, Dave Stewart, John Burkardt,
Uncovering a local trend in consumer eyetracking data 
Application of singular value decomposition in analyzing gaze
sequence data,
Proceedings of the 2018 Global Marketing Conference,
Tokyo, 10 March 2018,
fzsb_2018.pdf.

Marcus Garvie, John Burkardt, Jeff Morgan,
Simple finite element methods for approximating predatorprey
dynamics in two dimensions using MATLAB,
Bulletin of Mathematical Biology,
Volume 77, Number 3, 2015, pages 548578,
MR3327461.pdf.

Marcus Garvie, John Burkardt,
A new mathematical model for tiling finite regions of the plane
with polyominoes,
Contributions to Discrete Mathematics,
Volume 15, Number 2, July 2020, pages 95131
MR4217222.pdf.

Marcus Garvie, John Burkardt,
A new algorithm based on colouring arguments for identifying
impossible polyomino tiling problems,
Algorithms,
Volume 15, Number 2, 65, February 2022,
algorithms1500065.pdf.

Greg Hood, John Burkardt, Greg Foss,
Visualizing the visual system,
Neurocomputing,
Volume 3233(14), 2000, pages 801808,
hbf_2000.pdf.

Doug Jacobsen, Max Gunzburger, Todd Ringler, John Burkardt,
Janet Peterson,
Parallel algorithm for spherical Delaunay triangulations and spherical
centroidal Voronoi tessellations,
Geosciences Model Development,
Volume 6, 2013, pages 13531365,
jgrbp_2013.pdf.

Sangbum Kim, John Burkardt, Max Gunzburger, Janet Peterson,
ChiaRen Hu,
Effects of sample geometry on the dynamics and configuration of
vortices in mesoscopic superconductors,
Physical Review B,
Volume 76, 025509, 2007, 11 pages,
kbgph_2007.pdf.

Hugh MacMillan, Max Gunzburger, John Burkardt,
Meshfree firstorder system least squares,
Numerical Mathematics: Theory, Methods and Applications,
Volume 1, Number 1, 2008, pages 2943,
MR2401665.pdf.

Hoa Nguyen, John Burkardt, Max Gunzburger, Lili Ju, Yuki Saka,
Constrained CVT meshes and a comparison of triangular mesh
generators,
Computational Geometry: Theory and Applications,
Volume 42, Number 1, 2009, pages 119,
MR2455499.pdf.

Hoa Nguyen, Max Gunzburger, Lili Ju, John Burkardt,
Adaptive anisotropic meshing for steady convectiondominated problems,
Computer Methods in Applied Mechanics and Engineering,
Volume 198, Numbers 3740, pages 29642981, 1 August 2009,
MR2567853.pdf.

Mauro Perego, Max Gunzburger, John Burkardt,
Parallel finite element implementation for higherorder icesheet
models,
Journal of Glaciology,
Volume 58, Number 207, pages 7688, 2012,
pgb_2011.pdf.

Werner Rheinboldt, John Burkardt,
A locally parameterized continuation process,
ACM Transactions on Mathematical Software,
Volume 9, Number 2, June 1983, pages 215235,
MR715303.pdf.

Werner Rheinboldt, John Burkardt,
Algorithm 596: A program for a locally parameterized
continuation process,
ACM Transactions on Mathematical Software,
Volume 9, Number 2, June 1983, pages 236241,
rb_toms2_1983.pdf.

Vicente Romero, John Burkardt, Max Gunzburger, Janet Peterson,
Thiagaraja Krishnamurthy,
Initial application and evaluation of a promising new sampling
method for response surface generation: centroidal Voronoi
tessellation,
AIAA20032008,
44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference, Norfolk, Virginia, April 710, 2003,
rbgpk_2003.pdf.

Vicente Romero, John Burkardt, Max Gunzburger, Janet Peterson,
Initial evaluation of centroidal Voronoi tessellation for
statistical sampling and function integration,
Fourth International Symposium on Uncertainty Modeling and Analysis,
(ISUMA) 2003,
rbgp_2003.pdf.

Vicente Romero, John Burkardt, Max Gunzburger, Janet Peterson,
Initial evaluation of pure and "latinized" centroidal Voronoi
tessellation for nonuniform statistical sampling,
Sensitivity Analysis of Model Output (SAMO 2004) Conference,
Santa Fe, March 811, 2004,
rbgp_2004.pdf.

Vicente Romero, John Burkardt, Max Gunzburger, Janet Peterson,
Comparison of pure and "latinized" centroidal Voronoi
tessellation against various other statistical sampling methods,
Journal of Reliability Engineering and System Safety,
Volume 91, Numbers 1011, October/November 2006, pages 12661280
rbgp_ress_2006.pdf.

Yuki Saka, Max Gunzburger, John Burkardt,
Latinized, improved LHS, and CVT point sets in hypercubes,
International Journal of Numerical Analysis and Modeling,
Volume 4, Number 34, 2007, pages 729743,
MR2344066.pdf.

Miroslav Stoyanov, Max Gunzburger, John Burkardt,
Pink noise, 1/f^alpha noise, and their effect on solutions
of differential equations,
International Journal for Uncertainty Quantification,
Volume 1, Number 3, 2011, pages 257278,
MR2843294.pdf.

Catalin Trenchea, John Burkardt,
Refactorization of the midpoint rule,
Applied Mathematics Letters,
Volume 107, September 2020,
MR4092601.pdf.

Catalin Trenchea, John Burkardt,
Refactorization of the midpoint rule,
Technical Report TRMATH 2002,
Department of Mathematics,
University of Pittsburgh, 2020,
https://www.mathematics.pitt.edu/sites/default/files/midpoint3_technicalreport.pdf,
midpoint3_technicalreport.pdf.

HansWerner van Wyk, Max Gunzburger, John Burkardt, Miroslav Stoyanov,
Powerlaw noises over general domains and on nonstandard meshes,
SIAM/ASA Journal on Uncertainty Quantification,
Volume 3, Number 1, 2015, pages 269319,
MR3338005.pdf.

Feifei Xu, Max Gunzburger, John Burkardt, Qiang Du,
A multiscale implementation for the nonlocal peridynamics
model in one dimension,
Multiscale Modeling and Simulation,
Volume 14, Number 1, 2016, pages 398429.
MR3472006.pdf.

Feifei Xu, Max Gunzburger, John Burkardt,
A multiscale method for nonlocal mechanics and diffusion and
for the approximation of discontinuous functions,
Computer Methods in Applied Mechanics and Engineering,
Volume 307, 2016, pages 117143,
MR3511709.pdf.

Xiankui Zeng, Ming Ye, John Burkardt, Jichun Wu, Dong Wang,
Xiaobin Zhu,
Evaluating two sparse grid surrogates and two adaptation criteria for
groundwater Bayesian uncertainty quantification,
Journal of Hydrology,
Volume 535, April 2016, pages 120134,
zybww_2016.pdf.

Guannan Zhang, Clayton Webster, Max Gunzburger, John Burkardt,
A hyperspherical adaptive sparsegrid method for highdimensional
discontinuity detection,
SIAM Journal on Numerical Mathematics,
Volume 53, Number 3, 2015, pages 15081536,
MR3359679.pdf.

Guannan Zhang, Clayton Webster, Max Gunzburger, John Burkardt,
A hyperspherical adaptive sparsegrid method for highdimensional
discontinuity detection,
SIAM Review,
Volume 58, Number 3, 2016, pages 517551,
MR3532800.pdf.
Not published:

Xi Chen, Max Gunzburger, John Burkardt,
Optimal convergence rates for finite element methods in option
pricing under Heston's stochastic volatility model,
cbg_2014.pdf.

Max Gunzburger, John Burkardt,
Uniformity meastures for point samples in hypercubes,
gb_2004.pdf.

HansWerner van Wyk, Max Gunzburger, John Burkardt,
ClenshawCurtis type rules for integrals in statistics,
vgb_2016.pdf.
Last revised on 17 February 2022.