John Burkardt
Publications

• Jeff Borggaard, John Burkardt, John Burns, Eugene Cliff, Max Gunzburger, Hongchul Kim, Hyung-Chun 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 8-9, 1994,
  Birkhaeuser, Boston 1995,
  ISBN: 0-8176-3808-3,
  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, Hyung-Chun Lee,
  Reduced-order 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, Hyung-Chun Lee,
  Centroidal Voronoi tessellation-based reduced-order modeling of complex systems,
  SIAM Journal on Scientific Computing,
  Volume 28, Number 2, 2006, pages 459-484,
  MR2231716.pdf.
• John Burkardt, Max Gunzburger, Hyung-Chun Lee,
  POD and CVT-based reduced-order modeling of Navier-Stokes flows,
  Computer Methods in Applied Mechanics and Engineering,
  Volume 196, Number 1-3, 1 December 2006, pages 337-355,
  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 171-185,
  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: SAND2002-0099,
  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 3-4, 2007, pages 368-391,
  MR2344047.pdf.
• John Burkardt, Max Gunzburger, Wenju Zhao,
  High-precision computations of the weak Galerkin methods for the fourth-order 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 476-483,
  bhp_1986.pdf.
• John Burkardt, Wenlong Pei, Catalin Trenchea,
  A stress test for the midpoint time-stepping 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 111-126,
  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 A1389-A1411. 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 847-862.
• 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 315-320,
  ISBN-13: 978-9061916598
• 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 269-282,
  cwbhr_1988.pdf.
• Michael Eldred, John Burkardt,
  Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification,
  American Institute of Aeronautics and Astronautics,
  Paper 2009-0976,
  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 eye-tracking 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 predator-prey dynamics in two dimensions using MATLAB,
  Bulletin of Mathematical Biology,
  Volume 77, Number 3, 2015, pages 548-578,
  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 95-131
  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,
  algorithms-15-00065.pdf.
• Greg Hood, John Burkardt, Greg Foss,
  Visualizing the visual system,
  Neurocomputing,
  Volume 32-33(1-4), 2000, pages 801-808,
  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 1353-1365,
  jgrbp_2013.pdf.
• Sangbum Kim, John Burkardt, Max Gunzburger, Janet Peterson, Chia-Ren 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 first-order system least squares,
  Numerical Mathematics: Theory, Methods and Applications,
  Volume 1, Number 1, 2008, pages 29-43,
  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 1-19,
  MR2455499.pdf.
• Hoa Nguyen, Max Gunzburger, Lili Ju, John Burkardt,
  Adaptive anisotropic meshing for steady convection-dominated problems,
  Computer Methods in Applied Mechanics and Engineering,
  Volume 198, Numbers 37-40, pages 2964-2981, 1 August 2009,
  MR2567853.pdf.
• Mauro Perego, Max Gunzburger, John Burkardt,
  Parallel finite element implementation for higher-order ice-sheet models,
  Journal of Glaciology,
  Volume 58, Number 207, pages 76-88, 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 215-235,
  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 236-241,
  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,
  AIAA-2003-2008,
  44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia, April 7-10, 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 non-uniform statistical sampling,
  Sensitivity Analysis of Model Output (SAMO 2004) Conference, Santa Fe, March 8-11, 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 10-11, October/November 2006, pages 1266-1280
  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 3-4, 2007, pages 729-743,
  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 257-278,
  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 TR-MATH 20-02,
  Department of Mathematics,
  University of Pittsburgh, 2020,
  https://www.mathematics.pitt.edu/sites/default/files/midpoint3_technicalreport.pdf,
  midpoint3_technicalreport.pdf.
• Hans-Werner van Wyk, Max Gunzburger, John Burkardt, Miroslav Stoyanov,
  Power-law noises over general domains and on non-standard meshes,
  SIAM/ASA Journal on Uncertainty Quantification,
  Volume 3, Number 1, 2015, pages 269-319,
  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 398-429.
  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 117-143,
  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 120-134,
  zybww_2016.pdf.
• Guannan Zhang, Clayton Webster, Max Gunzburger, John Burkardt,
  A hyperspherical adaptive sparse-grid method for high-dimensional discontinuity detection,
  SIAM Journal on Numerical Mathematics,
  Volume 53, Number 3, 2015, pages 1508-1536,
  MR3359679.pdf.
• Guannan Zhang, Clayton Webster, Max Gunzburger, John Burkardt,
  A hyperspherical adaptive sparse-grid method for high-dimensional discontinuity detection,
  SIAM Review,
  Volume 58, Number 3, 2016, pages 517-551,
  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.
• Hans-Werner van Wyk, Max Gunzburger, John Burkardt,
  Clenshaw-Curtis type rules for integrals in statistics,
  vgb_2016.pdf.