Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators. - Francis X. Giraldo (Comput. Math. Appl., 2006)

High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere. - Francis X. Giraldo (J. Comput. Phys., 2006)

A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases. - Francis X. Giraldo; Marco Restelli (J. Comput. Phys., 2008)

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates. - Matthias Läuter; Francis X. Giraldo; Dörthe Handorf; Klaus Dethloff (J. Comput. Phys., 2008)

A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Modeling. - Marco Restelli; Francis X. Giraldo (SIAM J. Sci. Comput., 2009)

Klein-Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions. - Joseph M. Lindquist; Francis X. Giraldo; Beny Neta (Appl. Math. Comput., 2010)

Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling. - Francis X. Giraldo; Marco Restelli; Matthias Läuter (SIAM J. Sci. Comput., 2010)

High-order discontinuous element-based schemes for the inviscid shallow water equations: Spectral multidomain penalty and discontinuous Galerkin methods. - J. A. Escobar-Vargas; Peter J. Diamessis; Francis X. Giraldo (Appl. Math. Comput., 2012)

High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements. - Joseph M. Lindquist; Beny Neta; Francis X. Giraldo (Appl. Math. Comput., 2012)

Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: Limited-area mode. - James F. Kelly; Francis X. Giraldo (J. Comput. Phys., 2012)

An Element-Based Spectrally Optimized Approximate Inverse Preconditioner for the Euler Equations. - L. E. Carr III; Carlos F. Borges; Francis X. Giraldo (SIAM J. Sci. Comput., 2012)

Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments. - Andreas Müller 010; Jörn Behrens; Francis X. Giraldo; Volkmar Wirth (J. Comput. Phys., 2013)

Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA). - Francis X. Giraldo; James F. Kelly; Emil M. Constantinescu (SIAM J. Sci. Comput., 2013)

Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations. - Michal A. Kopera; Francis X. Giraldo (J. Comput. Phys., 2014)

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow. - Leonid Yelash; Andreas Müller 010; Mária Lukácová-Medvid'ová; Francis X. Giraldo; Volkmar Wirth (J. Comput. Phys., 2014)

Mass conservation of the unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations. - Michal A. Kopera; Francis X. Giraldo (J. Comput. Phys., 2015)

A parameter-free dynamic alternative to hyper-viscosity for coupled transport equations: Application to the simulation of 3D squall lines using spectral elements. - Simone Marras; Francis X. Giraldo (J. Comput. Phys., 2015)

Stabilized high-order Galerkin methods based on a parameter-free dynamic SGS model for LES. - Simone Marras; Murtazo Nazarov; Francis X. Giraldo (J. Comput. Phys., 2015)

Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations. - Daniel S. Abdi; Francis X. Giraldo (J. Comput. Phys., 2016)

Matrix-Free Polynomial-Based Nonlinear Least Squares Optimized Preconditioning and Its Application to Discontinuous Galerkin Discretizations of the Euler Equations. - L. E. Carr III; Carlos F. Borges; Francis X. Giraldo (J. Sci. Comput., 2016)

IMEX HDG-DG: a coupled implicit hybridized discontinuous Galerkin (HDG) and explicit discontinuous Galerkin (DG) approach for shallow water systems. - Shinhoo Kang; Francis X. Giraldo; Tan Bui-Thanh (CoRR, 2017)

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction. - Boris Bonev; Jan S. Hesthaven; Francis X. Giraldo; Michal A. Kopera (J. Comput. Phys., 2018)

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)

IMEX HDG-DG: A coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for shallow water systems. - Shinhoo Kang; Francis X. Giraldo; Tan Bui-Thanh (J. Comput. Phys., 2020)

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)

IMplicit-EXplicit Formulations for Discontinuous Galerkin Non-Hydrostatic Atmospheric Models. - Sohail R. Reddy; Maciej Waruszewski; Felipe A. V. de Braganca Alves; Francis X. Giraldo (CoRR, 2022)

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)

A physics-based open atmosphere boundary condition for height-coordinate atmospheric models. - James F. Kelly; Sohail R. Reddy; Francis X. Giraldo; P. Alex Reinecke; John T. Emmert; McArthur Jones; Stephen D. Eckermann (J. Comput. Phys., 2023)

Schur complement IMplicit-EXplicit formulations for discontinuous Galerkin non-hydrostatic atmospheric models. - Sohail R. Reddy; Maciej Waruszewski; Felipe A. V. de Braganca Alves; Francis X. Giraldo (J. Comput. Phys., 2023)

Comparison of adaptive mesh refinement techniques for numerical weather prediction. - Daniel S. Abdi; Ann S. Almgren; Francis X. Giraldo; Isidora Jankov (CoRR, 2024)

Multiscale Modeling Framework using Element-based Galerkin Methods for Moist Atmospheric Limited-Area Simulations. - Soonpil Kang; James F. Kelly; Anthony P. Austin; Francis X. Giraldo (CoRR, 2024)

A performance study of horizontally explicit vertically implicit (HEVI) time-integrators for non-hydrostatic atmospheric models. - Francis X. Giraldo; Felipe A. V. de Braganca Alves; James F. Kelly; Soonpil Kang; P. Alex Reinecke (J. Comput. Phys., 2024)

A GPU-accelerated simulation of rapid intensification of a tropical cyclone with observed heating. - Soonpil Kang; Francis X. Giraldo; Seth Camp (CoRR, 2025)