Research

My research interests are generally classified as scientific computation with an emphasis on the numerical solution of partial differential equations (with specific interest in wave propagation) and uncertainty quantification using high-order methods.

Publications

• 2021
  • S. Byrne and L. C. Wilcox and V. Churavy, "MPI.jl: Julia bindings for the Message Passing Interface," Proceedings of the JuliaCon Conferences, 68, 2021. DOI: 10.21105/jcon.00068.
  • J. E. Kozdon, B. A. Erickson, and L. C. Wilcox, "Hybridized summation-by-parts finite difference methods," Journal of Scientific Computing, vol. 87, no. 3, 2021. arXiv: 2002.00116. DOI: 10.1007/s10915-021-01448-5.
• 2019
  • J. E. Kozdon, L. C. Wilcox, T. Hagstrom, and J. W. Banks, "Robust approaches to handling complex geometries with Galerkin difference methods," Journal of Computational Physics, vol. 392, pp. 483–510, 2019. arXiv: 1806.06103; DOI: 10.1016/j.jcp.2019.04.031.
  • A. Müller, M. A. Kopera, S. Marras, L. C. Wilcox, T. Isaac, and F. X. Giraldo, "Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA," The International Journal of High Performance Computing Applications, vol. 33, no. 2, pp. 411–426, 2019. arXiv: 1511.01561; DOI: 10.1177/1094342018763966.
  • D. S. Abdi, F. X. Giraldo, E. M. Constantinescu, L. E. Carr III, L. C. Wilcox, T. C. Warburton, "Acceleration of the implicit-explicit non-hydrostatic unified model of the atmosphere (NUMA) on manycore processors," 2017, (submitted). The International Journal of High Performance Computing Applications, vol. 33, no. 2, pp. 242–267, 2019. arXiv: 1702.04316; DOI: 10.1177/1094342017732395.
  • N. Koeppen, I. M. Ross, L. C. Wilcox, and R. J. Proulx, "Fast mesh refinement in pseudospectral optimal control," Journal of Guidance, Control, and Dynamics, vol. 42, no. 4, pp. 711–722, 2019. arXiv: 1904.12992; DOI: 10.2514/1.G003904.
  • D. S. Abdi, L. C. Wilcox, T. Warburton, and F. X. Giraldo, "A GPU accelerated continuous and discontinuous Galerkin non-hydrostatic atmospheric model," The International Journal of High Performance Computing Applications, vol. 33, no. 1, 2019. DOI: 10.1177/1094342017694427.
  • J. Chan and L. C. Wilcox, "On discretely entropy stable weight-adjusted discontinuous Galerkin methods: Curvilinear meshes," Journal of Computational Physics, vol. 378, pp. 366–393, 2019. arXiv: 1805.10934; DOI: 10.1016/j.jcp.2018.11.010.
• 2018
  • J. E. Kozdon, L. C. Wilcox, "An energy stable approach for discretizing hyperbolic equations with nonconforming discontinuous Galerkin methods," Journal of Scientific Computing, vol. 76, no. 3, pp. 1742–1784, 2018. arXiv: 1706.00513; DOI: 10.1007/s10915-018-0682-1.
• 2017
  • W. Kang, O. Yakimenko, and L. Wilcox, "Optimal Control of UAVs Using the Sparse Grid Characteristic Method," in Proceedings of The 3rd International Conference on Control, Automation and Robotics (ICCAR 2017), (32% acceptance ratio), pp. 771–776, 2017. DOI: 10.1109/ICCAR.2017.7942802.
  • W. Kang and L. C. Wilcox, "Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations," Computational Optimization and Applications, vol. 68, no. 2, pp. 289–315, 2017. arXiv: 1507.04769; DOI: 10.1007/s10589-017-9910-0.
  • W. Kang and L. C. Wilcox, "Solving 1D conservation laws using Pontryagin's minimum principle," Journal of Scientific Computing, vol. 71, no. 1, pp.144–165, 2017. arXiv: 1605.04473; DOI: 10.1007/s10915-016-0294-6.
• 2016
  • A. Klöckner, L. C. Wilcox, and T. Warburton, "Array program transformation with Loo.py by example: High-order finite elements," in Proceedings of ARRAY '16: ACM SIGPLAN Workshop on Libraries, Languages, and Compilers for Array Programming, pp. 9–16, 2016. arXiv: 1604.08501; DOI: 10.1145/2935323.2935325.
  • R. Ye, M. V. de Hoop, C. L. Petrovitch, L. J. Pyrak-Nolte, and L. C. Wilcox "A discontinuous Galerkin method with a modified penalty flux for the propagation and scattering of acousto-elastic waves," Geophysical Journal International, vol. 205, no. 2, 2016. DOI: 10.1093/gji/ggw070.
  • J. E. Kozdon and L. C. Wilcox, "Stable coupling of nonconforming, high-order finite difference methods," SIAM Journal on Scientific Computing, vol. 38, no. 2, pp. A923–A952, 2016. arXiv: 1410.5746; DOI: 10.1137/15M1022823.
• 2015
  • W. Kang and L. C. Wilcox, "An example of solving HJB equations using sparse grid for feedback control," in 54th IEEE Conference on Decision and Control, 2015. DOI: 10.1109/CDC.2015.7402358.
  • T. Isaac, C. Burstedde, L. C. Wilcox, and O. Ghattas, "Recursive algorithms for distributed forests of octrees,” SIAM Journal on Scientific Computing, vol. 37, no. 5, pp. C497–C531, 2015. DOI: 10.1137/140970963.
  • L. C. Wilcox, G. Stadler, T. Bui-Thanh, and O. Ghattas, "Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method," Journal of Scientific Computing, vol. 63, no. 1, pp. 138–162, 2015. arXiv: 1311.6900; DOI: 10.1007/s10915-014-9890-5.
  • W. Kang and L. Wilcox, "A causality free computational method for HJB equations with application to rigid body satellites," in AIAA Guidance, Navigation, and Control Conference, American Institute of Aeronautics and Astronautics, Feb. 2015. DOI: 10.2514/6.2015-2009.
• 2013
  • X. He, E. Lee, L. Wilcox, R. Munipalli, and L. Pilon, "A high-order-accurate GPU-based radiative transfer equation solver for combustion and propulsion applications," Numerical Heat Transfer, Part B: Fundamentals, vol. 63, no. 6, pp. 457–484, 2013. DOI: 10.1080/10407790.2013.778669.
  • C. Burstedde, G. Stadler, L. Alisic, L. C. Wilcox, E. Tan, M. Gurnis, and O. Ghattas, "Large-scale adaptive mantle convection simulation," Geophysical Journal International, vol. 192, no. 3, pp. 889–906, 2013. DOI: 10.1093/gji/ggs070.
• 2012
  • T. Bui-Thanh, C. Burstedde, O. Ghattas, J. Martin, G. Stadler, and L. C. Wilcox, "Extreme-scale UQ for Bayesian inverse problems governed by PDEs," in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, ser. SC '12, Los Alamitos, CA, USA: IEEE Computer Society, 2012, 3:1–3:11. DOI: 10.1109/SC.2012.56.
  • J. Martin, L. C. Wilcox, C. Burstedde, and O. Ghattas, "A stochastic Newton MCMC method for largescale statistical inverse problems with application to seismic inversion," SIAM Journal on Scientific Computing, vol. 34, no. 3, A1460–A1487, 2012. DOI: 10.1137/110845598.
• 2011
  • C. Burstedde, L. C. Wilcox, and O. Ghattas, "p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees," SIAM Journal on Scientific Computing, vol. 33, no. 3, pp. 1103–1133, 2011. DOI: 10.1137/100791634.
  • H. P. Flath, L. C. Wilcox, V. Akçelik, J. Hill, B. van Bloemen Waanders, and O. Ghattas, "Fast algorithms for Bayesian uncertainty quantification in large-scale linear inverse problems based on low-rank partial Hessian approximations," SIAM Journal on Scientific Computing, vol. 33, no. 1, pp. 407–432, 2011. DOI: 10.1137/090780717.
• 2010
  • L. Alisic, M. Gurnis, G. Stadler, C. Burstedde, L. C. Wilcox, and O. Ghattas, "Slab stress and strain rate as constraints on global mantle flow," Geophysical Research Letters, vol. 37, p. L22308, 2010. DOI: 10.1029/2010GL045312.
  • L. C. Wilcox, G. Stadler, C. Burstedde, and O. Ghattas, "A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media," Journal of Computational Physics, vol. 229, pp. 9373–9396, 24 Dec. 2010. DOI: 10.1016/j.jcp.2010.09.008.
  • G. Stadler, M. Gurnis, C. Burstedde, L. C. Wilcox, L. Alisic, and O. Ghattas, "The Dynamics of Plate Tectonics and Mantle Flow: From Local to Global Scales," Science, vol. 329, no. 5995, pp. 1033–1038, 2010. DOI: 10.1126/science.1191223.
  • C. Burstedde, O. Ghattas, M. Gurnis, T. Isaac, G. Stadler, T. Warburton, and L. Wilcox, "Extreme-scale AMR," in Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, ser. SC '10, Washington, DC, USA: IEEE Computer Society, 2010, pp. 1–12. DOI: 10.1109/SC.2010.25.
  • J. S. Hesthaven, T. Warburton, C. Chauviere, and L. Wilcox, "High-order discontinuous Galerkin methods for computational electromagnetics and uncertainty quantification," in Scientific Computing in Electrical Engineering SCEE 2008, ser. Mathematics in Industry, J. Roos and L. R. Costa, Eds., vol. 14, 2010, pp. 403–412. DOI: 10.1007/978-3-642-12294-1_50.
• 2009
  • C. Burstedde, M. Burtscher, O. Ghattas, G. Stadler, T. Tu, and L. C. Wilcox, "ALPS: a framework for parallel adaptive PDE solution," in Journal of Physics: Conference Series, vol. 180, 2009, p. 012009. DOI: 10.1088/1742-6596/180/1/012009.
  • C. Burstedde, O. Ghattas, G. Stadler, T. Tu, and L. C. Wilcox, "Parallel scalable adjoint-based adaptive solution of variable-viscosity Stokes flow problems," Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 21–26, pp. 1691–1700, 2009, Advances in Simulation-Based Engineering Sciences — Honoring J. Tinsley Oden. DOI: 10.1016/j.cma.2008.12.015.
• 2008
  • C. Burstedde, O. Ghattas, M. Gurnis, G. Stadler, E. Tan, T. Tu, L. C. Wilcox, and S. Zhong, "Scalable adaptive mantle convection simulation on petascale supercomputers," in SC '08: Proceedings of the 2008 ACM/IEEE conference on Supercomputing, Piscataway, NJ, USA, 2008, pp. 1–15. DOI: 10.1109/SC.2008.5214248.
  • C. Burstedde, O. Ghattas, G. Stadler, T. Tu, and L. C. Wilcox, "Towards adaptive mesh PDE simulations on petascale computers," in TeraGrid'08, Las Vegas, NV, 2008. [preprint].
• 2007
  • C. Chauviere, J. S. Hesthaven, and L. C. Wilcox, "Efficient computation of RCS from scatterers of uncertain shapes," IEEE Transactions on Antennas and Propagation, vol. 55, no. 5, pp. 1437–1448, May 2007. DOI: 10.1109/TAP.2007.895629.
  • L. N. Olson, J. S. Hesthaven, and L. C. Wilcox, "Developments in overlapping Schwarz preconditioning of high-order nodal discontinuous Galerkin discretizations," in Domain decomposition methods in science and engineering XVI, ser. Lecture Notes in Computational Science and Engineering, vol. 55, Berlin: Springer, 2007, pp. 325–332. DOI: 10.1007/978-3-540-34469-8_39.
• 2005
  • R. Horvath, L. C. Wilcox, H. C. Pedersen, N. Skivesen, J. S. Hesthaven, and P. M. Johansen, "Analytical and numerical study on grating depth effects in grating coupled waveguide sensors," Applied Physics B: Lasers and Optics, vol. 81, pp. 65–73, 2005. DOI: 10.1007/s00340-005-1841-2.
• 2004
  • L. C. Wilcox, P. G. Dinesen, and J. S. Hesthaven, "Fast and accurate boundary variation method for multilayered diffraction optics," Journal of the Optical Society of America A, vol. 21, no. 5, pp. 757–769, May 2004. DOI: 10.1364/JOSAA.21.000757.
• 2002
  • T. Camp, J. Boleng, and L. Wilcox, "Location information services in mobile ad hoc networks," in Proceedings of the IEEE International Conference on Communications (ICC 2002), (40.8% acceptance ratio), New York City, NY, 2002, pp. 3318–3324. [preprint].
  • T. Camp, J. Boleng, B. Williams, L. Wilcox, and W. Navidi, "Performance evaluation of two location based routing protocols," in Proceedings of the IEEE 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2002), (20.5% acceptance ratio), New York City, NY, 2002, pp. 1678–1687. [preprint].
• 2001
  • J. Boleng, B. Williams, T. Camp, L. Wilcox, and W. Navidi, "Performance of location-based routing protocols for an ad hoc network," in Proceedings of the 11th Local and Metropolitan Area Networks Workshop (LANMAN 2001), Boulder, CO, Mar. 2001, pp. 98–101.

Recent Teaching

• AY21 Fall
  • MA3132: Partial Differential Equations and Integral Transforms
  • MA2121: Differential Equations

Life

Family

Here are links to my family's web sites. (I am trying to spread what little google juice I have.)

• Huxley Wilcox
• Eliot Wilcox
• Leigh Brodie

Swirlee

In my earlier years I had blue hair. My brother said that it looked like I got a swirlee in blue toilet water and thus gave me the nickname swirlee.

Tennis

Anyone for tennis? I am looking for a doubles partner.