Scalable adaptive mantle convection simulation on petascale supercomputers. - Carsten Burstedde; Omar Ghattas; Michael Gurnis; Georg Stadler; Eh Tan; Tiankai Tu; Lucas C. Wilcox; Shijie Zhong (SC, 2008)

Extreme-Scale AMR. - Carsten Burstedde; Omar Ghattas; Michael Gurnis; Tobin Isaac; Georg Stadler; Tim Warburton; Lucas C. Wilcox (SC, 2010)

A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media. - Lucas C. Wilcox; Georg Stadler; Carsten Burstedde; Omar Ghattas (J. Comput. Phys., 2010)

p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees. - Carsten Burstedde; Lucas C. Wilcox; Omar Ghattas (SIAM J. Sci. Comput., 2011)

Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations. - H. P. Flath; Lucas C. Wilcox; Volkan Akcelik; Judith Hill; Bart G. van Bloemen Waanders; Omar Ghattas (SIAM J. Sci. Comput., 2011)

Extreme-scale UQ for Bayesian inverse problems governed by PDEs. - Tan Bui-Thanh; Carsten Burstedde; Omar Ghattas; James Martin; Georg Stadler; Lucas C. Wilcox (SC, 2012)

A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion. - James Martin; Lucas C. Wilcox; Carsten Burstedde; Omar Ghattas (SIAM J. Sci. Comput., 2012)

An example of solving HJB equations using sparse grid for feedback control. - Wei Kang 001; Lucas C. Wilcox (CDC, 2015)

Discretely Exact Derivatives for Hyperbolic PDE-Constrained Optimization Problems Discretized by the Discontinuous Galerkin Method. - Lucas C. Wilcox; Georg Stadler; Tan Bui-Thanh; Omar Ghattas (J. Sci. Comput., 2015)

Recursive Algorithms for Distributed Forests of Octrees. - Tobin Isaac; Carsten Burstedde; Lucas C. Wilcox; Omar Ghattas (SIAM J. Sci. Comput., 2015)

Array program transformation with Loo.py by example: high-order finite elements. - Andreas Klöckner; Lucas C. Wilcox; Timothy C. Warburton (ARRAY@PLDI, 2016)

Stable Coupling of Nonconforming, High-Order Finite Difference Methods. - Jeremy E. Kozdon; Lucas C. Wilcox (SIAM J. Sci. Comput., 2016)

Mitigating the curse of dimensionality: sparse grid characteristics method for optimal feedback control and HJB equations. - Wei Kang 001; Lucas C. Wilcox (Comput. Optim. Appl., 2017)

Solving 1D Conservation Laws Using Pontryagin's Minimum Principle. - Wei Kang 001; Lucas C. Wilcox (J. Sci. Comput., 2017)

An Energy Stable Approach for Discretizing Hyperbolic Equations with Nonconforming Discontinuous Galerkin Methods. - Jeremy E. Kozdon; Lucas C. Wilcox (J. Sci. Comput., 2018)

Fast Mesh Refinement in Pseudospectral Optimal Control. - N. Koeppen; I. Michael Ross; Lucas C. Wilcox; Ronald J. Proulx (CoRR, 2019)

Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA. - Andreas Müller 010; Michal A. Kopera; Simone Marras; Lucas C. Wilcox; Tobin Isaac; Francis X. Giraldo (Int. J. High Perform. Comput. Appl., 2019)

Acceleration of the IMplicit-EXplicit nonhydrostatic unified model of the atmosphere on manycore processors. - Daniel S. Abdi; Francis X. Giraldo; Emil M. Constantinescu; Lester E. Carr; Lucas C. Wilcox; Timothy C. Warburton (Int. J. High Perform. Comput. Appl., 2019)

A GPU-accelerated continuous and discontinuous Galerkin non-hydrostatic atmospheric model. - Daniel S. Abdi; Lucas C. Wilcox; Timothy C. Warburton; Francis X. Giraldo (Int. J. High Perform. Comput. Appl., 2019)

On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes. - Jesse Chan; Lucas C. Wilcox (J. Comput. Phys., 2019)

Robust approaches to handling complex geometries with Galerkin difference methods. - Jeremy E. Kozdon; Lucas C. Wilcox; Thomas M. Hagstrom; Jeffrey W. Banks (J. Comput. Phys., 2019)

Entropy Stable Discontinuous Galerkin Methods for Balance Laws in Non-Conservative Form: Applications to Euler with Gravity. - Maciej Waruszewski; Jeremy E. Kozdon; Lucas C. Wilcox; Thomas H. Gibson; Francis X. Giraldo (CoRR, 2021)

Hybridized Summation-by-Parts Finite Difference Methods. - Jeremy E. Kozdon; Brittany A. Erickson; Lucas C. Wilcox (J. Sci. Comput., 2021)

Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: Applications to the Euler equations with gravity. - Maciej Waruszewski; Jeremy E. Kozdon; Lucas C. Wilcox; Thomas H. Gibson; Francis X. Giraldo (J. Comput. Phys., 2022)

An energy stable high-order cut cell discontinuous Galerkin method with state redistribution for wave propagation. - Christina G. Taylor; Lucas C. Wilcox; Jesse Chan (J. Comput. Phys., 2025)