- Lucas Charles Wilcox
- Assistant Professor (CV)
- Naval Postgraduate School
Department of Applied Mathematics
833 Dyer Road; Building 232, SP-262
Monterey, California 93943
United States of America
- +1 (831) 656-3249
- +1 (720) 257-9799
- lwilcox@nps.edu
- me@lucaswilcox.com
- Google Scholar
- A86F 3413 3871 6AF3 7938 8941 8F37 791F 87D1 85DA
Teaching
- AY16 Q1
- MA2121: Differential Equations (two segments)
- AY15 Q3
- MA4261: Parallel Programming (NPS internal link)
- AY15 Q1
- MA2121: Differential Equations (two segments)
- AY14 Q3
- MA4261: Parallel Programming (NPS internal link)
- MA2121: Differential Equations
- AY13 Q4
- MA3232: Numerical Analysis
- MA2121: Differential Equations
- AY13 Q1
- MA1114: Single Variable Calculus II
- MA1113: Single Variable Calculus I
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
- Current
- W. Kang and L. C. Wilcox, "Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feeback control and HJB equations," 2015, (submitted) arxiv:1507.04769.
- J. E. Kozdon and L. C. Wilcox, Provably stable, general purpose projection operators for high-order finite difference methods, (submitted) arxiv:1410.5746.
- 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, (accepted), 2015.
- 2015
- 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. 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. 012 009. 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.
Life
Family
Here are links to my family's web sites. (I am trying to spread what little google juice I have.)
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.