Basis Functions for Triangular and Quadrilateral High-Order Elements. - Timothy C. Warburton; Spencer J. Sherwin; George E. Karniadakis (SIAM J. Sci. Comput., 1999)

Arbitrary Lagrangian Eulerian Analysis of a Bidirectional Micro-Pump Using Spectral Elements. - Ali Beskok; Timothy C. Warburton (Int. J. Comput. Eng. Sci., 2001)

Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method. - R. H. W. Hoppe; Guido Kanschat; Tim Warburton (SIAM J. Numer. Anal., 2008)

Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes. - Timothy Warburton; Thomas M. Hagstrom (SIAM J. Numer. Anal., 2008)

Nodal discontinuous Galerkin methods on graphics processors. - Andreas Klöckner; Tim Warburton; Jeff Bridge; Jan S. Hesthaven (J. Comput. Phys., 2009)

Exact Non-Reflecting Boundary Conditions on Perturbed Domains and hp-Finite Elements. - Tommy L. Binford; David P. Nicholls; Nilima Nigam; Tim Warburton (J. Sci. Comput., 2009)

The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem. - Annalisa Buffa; Ilaria Perugia; Tim Warburton (J. Sci. Comput., 2009)

Complete Radiation Boundary Conditions: Minimizing the Long Time Error Growth of Local Methods. - Thomas M. Hagstrom; Timothy Warburton (SIAM J. Numer. Anal., 2009)

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

Radiation boundary conditions for time-dependent waves based on complete plane wave expansions. - Thomas M. Hagstrom; Timothy Warburton; Dan Givoli (J. Comput. Appl. Math., 2010)

High-Order Discontinuous Galerkin Methods by GPU Metaprogramming - Andreas Klöckner; Timothy Warburton; Jan S. Hesthaven (CoRR, 2012)

Solving Wave Equations on Unstructured Geometries - Andreas Klöckner; Timothy Warburton; Jan S. Hesthaven (CoRR, 2013)

A Low-Storage Curvilinear Discontinuous Galerkin Method for Wave Problems. - Tim Warburton (SIAM J. Sci. Comput., 2013)

OCCA: A unified approach to multi-threading languages. - David S. Medina; Amik St.-Cyr; Timothy Warburton (CoRR, 2014)

High-Order Finite-differences on multi-threaded architectures using OCCA. - David S. Medina; Amik St.-Cyr; Timothy Warburton (CoRR, 2014)

hp-finite element trace inequalities for the pyramid. - Jesse Chan; Tim Warburton (Comput. Math. Appl., 2015)

A Comparison of High Order Interpolation Nodes for the Pyramid. - Jesse Chan; Timothy C. Warburton (SIAM J. Sci. Comput., 2015)

Residual-Based Adaptivity and PWDG Methods for the Helmholtz Equation. - Shelvean Kapita; Peter Monk 001; Timothy Warburton (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)

A GPU accelerated level set reinitialization for an adaptive discontinuous Galerkin method. - Ali Karakus; Timothy C. Warburton; M. H. Aksel; Cuneyt Sert (Comput. Math. Appl., 2016)

GPU Acceleration of Hermite Methods for the Simulation of Wave Propagation. - Arturo Vargas; Jesse Chan; Thomas M. Hagstrom; Timothy Warburton (CoRR, 2016)

GPU performance analysis of a nodal discontinuous Galerkin method for acoustic and elastic models. - Axel Modave; Amik St.-Cyr; Tim Warburton (Comput. Geosci., 2016)

GPU-accelerated discontinuous Galerkin methods on hybrid meshes. - Jesse Chan; Zheng Wang; Axel Modave; Jean-François Remacle; Timothy C. Warburton (J. Comput. Phys., 2016)

GPU accelerated spectral finite elements on all-hex meshes. - Jean-François Remacle; R. Gandham; Tim Warburton (J. Comput. Phys., 2016)

Orthogonal Bases for Vertex-Mapped Pyramids. - Jesse Chan; Timothy C. Warburton (SIAM J. Sci. Comput., 2016)

A Short Note on a Bernstein-Bezier Basis for the Pyramid. - Jesse Chan; Tim Warburton (SIAM J. Sci. Comput., 2016)

On the penalty stabilization mechanism for upwind discontinuous Galerkin formulations of first order hyperbolic systems. - Jesse Chan; Timothy C. Warburton (Comput. Math. Appl., 2017)

Reduced storage nodal discontinuous Galerkin methods on semi-structured prismatic meshes. - Jesse Chan; Zheng Wang; Russell J. Hewett; Timothy C. Warburton (Comput. Math. Appl., 2017)

Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes. - Jesse Chan; Russell J. Hewett; Timothy Warburton (SIAM J. Sci. Comput., 2017)

Weight-Adjusted Discontinuous Galerkin Methods: Wave Propagation in Heterogeneous Media. - Jesse Chan; Russell J. Hewett; Timothy Warburton (SIAM J. Sci. Comput., 2017)

GPU-Accelerated Bernstein-Bézier Discontinuous Galerkin Methods for Wave Problems. - Jesse Chan; Timothy C. Warburton (SIAM J. Sci. Comput., 2017)

GPU Acceleration of a High-Order Discontinuous Galerkin Incompressible Flow Solver. - Ali Karakus; Noel Chalmers; Kasia Swirydowicz; Timothy Warburton (CoRR, 2018)

An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs. - Niklas Wintermeyer; Andrew R. Winters; Gregor J. Gassner; Timothy Warburton (J. Comput. Phys., 2018)

Low-Order Preconditioning of High-Order Triangular Finite Elements. - Noel Chalmers; Timothy C. Warburton (SIAM J. Sci. Comput., 2018)

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)

Acceleration of tensor-product operations for high-order finite element methods. - Kasia Swirydowicz; Noel Chalmers; Ali Karakus; Tim Warburton (Int. J. High Perform. Comput. Appl., 2019)

Discontinuous Galerkin discretizations of the Boltzmann-BGK equations for nearly incompressible flows: Semi-analytic time stepping and absorbing boundary layers. - Ali Karakus; Noel Chalmers; Jan S. Hesthaven; Tim Warburton (J. Comput. Phys., 2019)

A GPU accelerated discontinuous Galerkin incompressible flow solver. - Ali Karakus; Noel Chalmers; Kasia Swirydowicz; Tim Warburton (J. Comput. Phys., 2019)

Leapfrog Time-Stepping for Hermite Methods. - Arturo Vargas; Thomas M. Hagstrom; Jesse Chan; Tim Warburton (J. Sci. Comput., 2019)

Portable high-order finite element kernels I: Streaming Operations. - Noel Chalmers; Tim Warburton (CoRR, 2020)

Scalability of high-performance PDE solvers. - Paul F. Fischer; Misun Min; Thilina Rathnayake; Som Dutta; Tzanio V. Kolev; Veselin Dobrev; Jean-Sylvain Camier; Martin Kronbichler 002; Timothy C. Warburton; Kasia Swirydowicz; Jed Brown (Int. J. High Perform. Comput. Appl., 2020)

Efficient exascale discretizations: High-order finite element methods. - Tzanio V. Kolev; Paul F. Fischer; Misun Min; Jack J. Dongarra; Jed Brown; Veselin Dobrev; Tim Warburton; Stanimire Tomov; Mark S. Shephard; Ahmad Abdelfattah; Valeria Barra; Natalie Beams; et al. (Int. J. High Perform. Comput. Appl., 2021)

GPU algorithms for Efficient Exascale Discretizations. - Ahmad Abdelfattah; Valeria Barra; Natalie Beams; Ryan Bleile; Jed Brown; Jean-Sylvain Camier; Robert Carson; Noel Chalmers; Veselin Dobrev; Yohann Dudouit; Paul F. Fischer; Ali Karakus; et al. (Parallel Comput., 2021)

Initial Guesses for Sequences of Linear Systems in a GPU-Accelerated Incompressible Flow Solver. - Anthony P. Austin; Noel Chalmers; Tim Warburton (SIAM J. Sci. Comput., 2021)

Optimization of Full-Core Reactor Simulations on Summit. - Misun Min; Yu-Hsiang Lan; Paul F. Fischer; Elia Merzari; Stefan Kerkemeier; Malachi Phillips; Thilina Rathnayake; April Novak; Derek Gaston; Noel Chalmers; Tim Warburton (SC, 2022)

A local discontinuous Galerkin level set reinitialization with subcell stabilization on unstructured meshes. - Ali Karakus; Noel Chalmers; Timothy C. Warburton (Comput. Math. Appl., 2022)

HipBone: A performance-portable GPU-accelerated C++ version of the NekBone benchmark. - Noel Chalmers; Abhishek Mishra; Damon McDougall; Tim Warburton (CoRR, 2022)

On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows. - Jesse Chan; Hendrik Ranocha; Andrés M. Rueda-Ramírez; Gregor Gassner; Tim Warburton (CoRR, 2022)

Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations. - Jesse Chan; Yimin Lin; Tim Warburton (J. Comput. Phys., 2022)

NekRS, a GPU-accelerated spectral element Navier-Stokes solver. - Paul F. Fischer; Stefan Kerkemeier; Misun Min; Yu-Hsiang Lan; Malachi Phillips; Thilina Rathnayake; Elia Merzari; Ananias Tomboulides; Ali Karakus; Noel Chalmers; Tim Warburton (Parallel Comput., 2022)

Exascale Multiphysics Nuclear Reactor Simulations for Advanced Designs. - Elia Merzari; Steven P. Hamilton; Thomas M. Evans 001; Misun Min; Paul F. Fischer; Stefan Kerkemeier; Jun Fang 005; Paul K. Romano; Yu-Hsiang Lan; Malachi Phillips; Elliott Biondo; Katherine Royston; et al. (SC, 2023)

HipBone: A performance-portable graphics processing unit-accelerated C++ version of the NekBone benchmark. - Noel Chalmers; Abhishek Mishra; Damon McDougall; Tim Warburton (Int. J. High Perform. Comput. Appl., 2023)

A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method. - Sophia Julia Feriani; Matthias Cosnefroy; Allan Peter Engsig-Karup; Tim Warburton; Finnur Pind; Cheol-Ho Jeong (CoRR, 2024)

Exascale Simulations of Fusion and Fission Systems. - Misun Min; Yu-Hsiang Lan; Paul F. Fischer; Elia Merzari; Tri Nguyen; Haomin Yuan; Patrick C. Shriwise; Stefan Kerkemeier; Andrew Davis; Aleksandr Dubas; Rupert Eardly; Rob J. Akers; et al. (CoRR, 2024)

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics. - Anders Melander; Emil Strøm; Finnur Pind; Allan P. Engsig-Karup; Cheol-Ho Jeong; Tim Warburton; Noel Chalmers; Jan S. Hesthaven (Int. J. High Perform. Comput. Appl., 2024)

Stopping Criteria for the Conjugate Gradient Algorithm in High-Order Finite Element Methods. - Yichen Guo; Eric de Sturler; Tim Warburton (SIAM J. Sci. Comput., 2025)

An Adaptive Mixed Precision and Dynamically Scaled Preconditioned Conjugate Gradient Algorithm. - Yichen Guo; Eric de Sturler; Tim Warburton (CoRR, 2025)