Lucas C Wilcox

Research Interests

My interests are generally classified as scientific computation with an emphasis on the numerical solution of partial differential equations and uncertianty quantification using high-order methods.

Currently my avenues of research include developing methods for large-scale uncertainty quantification for inverse problems involving pdes, the development of local time-stepping methods for discontinuous Galerkin methods and the development of adaptive finite element and discontinuous Galerkin frameworks for large-scale parallel computing.

Publication List

Ph.D. Thesis

L. C. Wilcox. High-Order Accurate Methods for Solving the Time-Harmonic Maxwell’s Equations. Ph.D. in Applied Mathematics, Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, 2006. [bib]

Journal Articles

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. (In Press) [doi]
C. Chauviere, J. S. Hesthaven, and L. C. Wilcox. Efficient computation of RCS from scatterers of uncertain shapes. IEEE Transactions on Antennas and Propagation, 55(5):1437–1448, May 2007. [bib] [pdf] [doi]
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, 81:65–73, 2005. [bib] [pdf] [doi]
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, 21(5):757–769, May 2004. [bib] [pdf] [doi]

Conference Proceedings

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, pages 1–15, Piscataway, NJ, USA, 2008. Gordon Bell Prize finalist. [bib] [pdf] [doi]
J. S. Hesthaven, T. Warburton, C. Chauviere and L. Wilcox. High-order discontinuous Galerkin methods for computational electromagnetics and uncertainty quantification. In Proceedings of 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), Hensinki University of Technology, Hensinki, Finland, 2008. [bib] [pdf]
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, USA, 2008. [bib] [pdf]
C. Chauviere, J. S. Hesthaven, L. Lurati, and L. C. Wilcox. DG-FEM for CEM with uncertainty. In Proceedings of 23rd International Review of Progress in Applied Computational Electromagnetics, Verona, Italy, March 2007. [bib]
J. S. Hesthaven, L. N. Olson, 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, volume 55 of Lecture Notes in Computational Science and Engineering, pages 325–332. Springer, Berlin, 2007. [bib] [pdf] [doi]
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), pages 3318–3324, 2002. [bib] [pdf]
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), pages 1678–1687, 2002. [bib] [pdf]
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), pages 98–101, March 2001. [bib]

Technical Reports

B. G. van Bloemen Waanders, R. A. Bartlett, S. S. Collis, E. R. Keiter, C. C. Ober, T. M. Smith, V. Akcelik, O. Ghattas, J. C. Hill, M. Berggren, M. Heinkenschloss, and L. C. Wilcox. Sensitivity technologies for large scale simulation. Technical Report SAND2004-6574, Sandia National Laboratory, PO Box 5800, Albuquerque, NM 87185-5800, 2004. (I wrote chapter 11) [bib] [pdf]

Presentations

2008 Oct. Parallel Adaptive Mantle Convection Simulation, Poster, Center for Subsurface Modeling Affiliates Meeting, Austin, TX.
2008 Sep. Parallel Adaptive Mantle Convection Simulation, Poster Mathematical and Computational Issues in Solid Earth Geosciences, Santa Fe, NM.
2008 Jul. Parallel Adaptive Solution of Mantle Convection Problems, 2008 SIAM Annual Meeting, San Diego, CA.
2008 May. Towards Adaptive Petascale Simulations of Geophysical Phenomena, Scientific Computing Seminar, Division of Applied Mathematics, Brown University, Providence, RI.
2008 Feb. Towards Petascale Simulations of Geophysical Phenomena, Colloquia, Department of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM
2007 Feb. Occam meets Bayes: Bridging the Divide, Poster, SIAM Conference on Computational Science and Engineering, Costa Mesa, CA.
2006 Oct. hp-Adaptive Solutions of the Time-Harmonic Maxwell’s Equations Using a Nodal Discontinuous Galerkin Method, ICES Seminar, The University of Texas at Austin, Austin, TX.
2006 Jul. Sledge++ — A discontinuous Galerkin finite element discretization package, 7th World Congress on Computational Mechanics, Los Angeles, CA.
2005 Nov. Implementation and examples using Sledge++ (a high-order nodal discontinuous Galerkin library), CAAM Graduate Seminar, Computational and Applied Mathematics, Rice University, Houston, TX.
2005 Aug. Adjoint based a posteriori error analysis for a 3D high order nodal discontinuous Galerkin method, Student Internship Symposium, Sandia National Laboratories, Albuquerque, NM.
2004 Aug. Adjoint based a posteriori error analysis applied to a high order nodal discontinuous Galerkin method, Student Internship Symposium, Sandia National Laboratories, Albuquerque, NM.

Software Developed

Lead developer of pFudg, 2007 – present, A MPI based library for solving time-dependent hyperbolic partial differential equations using quadrature based discontinuous Galerkin methods, naming conventions follow the matlab reference implementation NUDG where it makes sense.
Co-developer of judg, 2007 – present, A Java implementation of the nodal discontinuous Galerkin method described in Nodal Discontinuous Galerkin Methods.
Co-developer of the ALPS Toolkit, 2007 – present, A MPI based framework for large-scale h-adaptive finite element framework with applications in geosciences. Including p4est, a forest of octrees library to support parallel h-adaptivity and mangll, a high-order h-adaptive continuous and discontinuous finite element discretization library.
Co-developer of Rhea, 2007 – present, A mantle convection code using ALPS.
Co-developer of Sledge++, 2003 – present, A object oriented C++ library for conforming and nonconforming hp-adaptive discontinuous Galerkin methods.

Reading Groups

Uncertainty Quantification