Frank Giraldo
Distinguished Professor of Applied Mathematics
Naval Postgraduate School
Monterey, California 93943 USA
Book
Journal Articles
Francis X. Giraldo. An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases: Analysis, Algorithms, and Applications, Springer Texts in Computational Science and Engineering, Series Volume 24, ISBN: 978-3-030-55068-4 (2020), (Springer). There is a corresponding GitHub site for the book containing Julia and Matlab code (GitHub).
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2024
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James F. Kelly, Felipe A. V. B. Alves, Stephen D. Eckermann, Francis X. Giraldo, P. Alex Reinecke, John T. Emmert, A nonhydrostatic mass-conserving dynamical core for deep atmospheres of variable composition, (submitted November 19, 2024) (arXiv)(ResearchGate).
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Soonpil Kang, James F. Kelly, Anthony P. Austin, and Francis X. Giraldo, Multiscale modeling framework using element-based Galerkin methods for moist atmospheric limited-area simulations, Journal of Advances in Modeling Earth Systems (revised and resubmitted November 15, 2024) (arXiv)(ResearchGate).
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Yassine Tissaoui, Stephen Guimond, Francis X. Giraldo, Simone Marras, Accelerating simulations of tropical cyclones using adaptive mesh refinement, Journal of the Atmospheric Sciences (DOI:10.13140/RG.2.2.35151.70563) (submitted October 28, 2024)(arXiv)(ResearchGate). ​
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Daniel S. Abdi, Ann Almgren, Francis X. Giraldo, and Isidora Jankov, Comparison of adaptive mesh refinement techniques for numerical weather prediction, Monthly Weather Review (revised and resubmitted August 22, 2024) (arXiv) (ResearchGate).
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Francis X. Giraldo, Felipe A. V. B. Alves, James F. Kelly, Soonpil Kang, and P. Alex Reinecke, A performance study of horizontally explicit vertically implicit (HEVI) time-integrators for non-hydrostatic atmospheric models, Journal of Computational Physics Vol 515 113275 (2024) (JCP)(arXiv) (ResearchGate).
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2023​
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Sohail Reddy, Maciej Waruszewski, Felipe A. V. de Braganca Alves, Francis X. Giraldo, Schur complement IMplicit-EXplicit formulations for discontinuous Galerkin non-hydrostatic atmospheric models, Journal of Computational Physics Vol 491 112361 (2023)(JCP)(ResearchGate).
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James F. Kelly, Sohail Reddy, Francis X. Giraldo, P. Alex Reinecke, John T. Emmert, MacArthur Jones Jr., Stephen D. Eckermann, A physics-based open atmosphere boundary condition for heigh-coordinate atmospheric models, Journal of Computational Physics Vol 482 112044 (2023) (JCP)(ResearchGate).
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A. N. Souza, J. He, T. Bischoff, M. Waruszewski, L. Novak, V. Barra, T. Gibson, A. Sridhar, S. Kandala, S. Byrne, L. C. Wilcox, J. Kozdon, F. X. Giraldo, O. Knoth, J. Marshall, R. Ferrari, T. Schneider, The flux-differencing discontinuous Galerkin method applied to an idealized fully compressible nonhydrostatic dry atmosphere, Journal of Advances in Modeling Earth Systems Vol 15 Issue 4 (2023) (AGU Pubs)(ResearchGate).
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Yassine Tissaoui, Simone Marras, Annalisa Quaini, Felipe A. V. de Braganca Alves, Francis X. Giraldo, A non-column based, fully unstructured implementation of Kessler's microphysics with warm rain using continuous and discontinuous spectral elements, Journal of Advances in Modeling Earth Systems Vol 15 Issue 3 (2023) (AGU Pubs)(arXiv)(ResearchGate).
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​Michal A. Kopera, Yao Gahounzo, Ellyn M.Enderlin, Francis X. Giraldo, and Wieslaw Maslowski. Non-hydrostatic Unified Model of the Ocean (NUMO) with application to ice/ocean interaction modeling, International Journal on Geomathematics Vol 14 Number 2 (2023) (Springer Nature)(ResearchGate).​
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2022​​​
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Md Badrul Hasan, Stephen R. Guimond, Meilin Yu, Sohail Reddy, Francis X. Giraldo, The effects of numerical dissipation on hurricane rapid intensification with observational heating, Journal of Advances in Modeling Earth Systems Vol 14 Issue 8 (2022) (ResearchGate).
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Maciej Waruszewski, Jeremy E. Kozdon, Lucas C. Wilcox, Thomas H. Gibson, Francis X. Giraldo. Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: applications to Euler with gravity, Journal of Computational Physics Vol 468 111507 (2022) (JCP)(arXiv)(ResearchGate).
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Akshay Sridhar, Yassine Tissaoui, Simone Marras, Zhaoyi Shen, Charles Kawczynski, Simon Byrne, Kiran Pamnany, Maciej Waruszewski, Thomas H. Gibson, Jeremy E. Kozdon, Valentin Churavy, Lucas C. Wilcox, Francis X. Giraldo, and Tapio Schneider. Large-eddy simulations with ClimateMachine: a new open-source code for atmospheric simulations on GPUs and CPUs, Geoscientific Model Development, gmd-2021-335 (2022) (GMD)(arXiv)(ResearchGate).
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2021​​
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Sohail Reddy, Yassine Tissaoui, Felipe A. V. de Braganca Alves, Simone Marras, Francis X. Giraldo, Comparison of sub-grid scale models for large-eddy simulation using a high-order spectral element approximation of the compressible Navier-Stokes equations at low Mach number, Journal of Computational Physics (submitted 2021) (arXiv)(ResearchGate).
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2020
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Brent Lunghino, Adrian F. Santiago Tate, Jenny Suckale, Simone Marras, Francis X. Giraldo, Miho Mazereeuw,and Abdul Muhari, The protective benefits of tsunami mitigation parks and ramifications for their strategic design, Proceedings of the National Academy of Science, https://doi.org/10.1073/pnas.1911857117 (2020) (PNAS)(News Articles)(ResearchGate).
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S. Kang, F.X. Giraldo, and T. Bui-Thanh, IMEX HDG-DG: A coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for shallow water systems, Journal of Computational Physics, Vol. 401, 109010 (2020) (ResearchGate)(arXiv).
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T.H. Yi and F.X. Giraldo, Vertical discretization for a nonhydrostatic atmospheric model based on high-order spectral elements, Monthly Weather Review Vol. 148, 415-436 (2020) (ResearchGate).
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2018
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B. Bonev, J.S. Hesthaven, F.X. Giraldo, and M.A. Kopera, Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction, Journal of Computational Physics, Vol. 362, 425-448 (2018) (ResearchGate)(PDF and Movies).
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Gianmarco Mengaldo, Andrzej Wyszogrodzki, Michail Diamantakis, Sarah-Jane Lock, Francis X. Giraldo, Nils P. Wedi, Current and emerging time-integration strategies in global numerical weather and climate prediction, Archives of Computational Methods in Engineering, https://doi.org/10.1007/s11831-018-9261-8 (2018) (ResearchGate).
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S. Marras, M. Kopera, E.M. Constantinescu, J. Suckale, F.X. Giraldo, A continuous/discontinuous Galerkin solution of the shallow water equations with dynamic viscosity, high-order wetting and drying, and implicit time integration, Advances in Water Resources, Vol. 114, 45-63 (2018). (ResearchGate)(arXiv).
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A. Mueller, M. Kopera, S. Marras, L. Wilcox, T. Isaac, F.X. Giraldo, Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA, International Journal for High-Performance Computing Applications, https://doi.org/10.1177/1094342018763966 (2018) (ResearchGate)(arXiv).
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2017
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D.S. Abdi, F.X. Giraldo, E.M. Constantinescu, L.E. Carr III, L. Wilcox, T. Warburton, Acceleration of the Implicit-Explicit Non-hydrostatic Unified Model of the Atmosphere (NUMA) on Manycore Processors, International Journal for High-Performance Computing Applications, https://doi.org/10.1177/1094342017732395 (2017) (ResearchGate)(arXiv).
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J. Carman, T. Clune, F.X. Giraldo, M. Govett, B. Gross, A. Kamrath, T. Lee, D. McCarren, J. Michalakes, S. Sandgathe, T. Whitcomb, Position Paper on High Performance Computing Needs in Earth System Prediction, National Earth System Prediction Capability (2017) (PDF)(ResearchGate).
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D.S. Abdi, L. Wilcox, T. Warburton, F.X. Giraldo, A GPU-accelerated continuous and discontinuous Galerkin non-hydrostatic atmospheric model, International Journal for High-Performance Computing Applications, https://doi.org/10.1177/1094342017694427 (2017) (ResearchGate).
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2016
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S. Guimond, J. Reisner, S. Marras, and F.X. Giraldo, The impacts of numerical schemes on asymmetric hurricane intensification, Journal of the Atmospheric Sciences, Vol. 73, 4661–4684 (2016) (ResearchGate).
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E. Hendricks, M.A. Kopera, F.X. Giraldo, Melinda S. Peng, James D. Doyle, and Qingfang Jiang, Evaluation of the utility of static and adaptive mesh refinement for idealized tropical cyclone problems in a spectral element shallow water model, Monthly Weather Review, Vol. 144, 3697–3724 (2016) (ResearchGate).
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D.S. Abdi and F.X. Giraldo, Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations, Journal of Computational Physics, Vol. 320, 46-68 (2016) (ResearchGate).
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G. Theurich, C. DeLuca, T. Campbell, F. Liu, K. Saint, M. Vertenstein, J. Chen, R. Oehmke, J. Doyle, T. Whitcomb, A. Wallcraft, M. Iredell, T. Black, A. DaSilva, T. Clune, R. Ferraro, P. Li, M. Kelley, I. Aleinov, V. Balaji, N. Zadeh, R. Jacob, B. Kirtman, F.X. Giraldo, D. McCarren, S. Sandgathe, S. Peckham, R. Dunlap, The Earth System Prediction Suite: towards a coordinated U.S. modeling capability, Bulletin of the American Meteorological Society, Vol. 97, Issue 7, 1229-1247 (2016) (ResearchGate).
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S. Marras, J.F. Kelly, M. Moragues, A. Mueller, M.A. Kopera, M. Vazquez, F.X. Giraldo, G. Houzeaux, O. Jorba, A review of element-based Galerkin methods for numerical weather prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin, Archives of Computational Methods in Engineering, Vol. 23, 673–722 (2016) (ResearchGate).
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2015
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M. Yu, F.X. Giraldo, M. Peng, Z.J. Wang, Localized artificial viscosity stabilization of discontinuous Galerkin methods for nonhydrostatic mesoscale atmospheric modeling, Monthly Weather Review, Vol. 143, 4823-4845 (2015) (ResearchGate).
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S. Marras, M. Nazarov, and F.X. Giraldo, A conservative, consistent, and grid adaptive stabilized spectral element method based on a dynamic LES model for the compressible Euler Equations: the case of low Mach stratified flow, Journal of Computational Physics, Vol. 301, 77-101 (2015) (ResearchGate).
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L.E., Carr, C.F. Borges, and F.X. Giraldo, A matrix-free polynomial-based nonlinear least-squares optimized preconditioner and its application to discontinuous Galerkin discretization of the Euler equations, Journal of Scientific Computing, Vol. 66, 917-940 (2015) (ResearchGate).
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M.A. Kopera and F.X. Giraldo, Mass conservation of unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations, Journal of Computational Physics, Vol 297, 90-103 (2015) (ResearchGate).
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S. Marras, and F.X. Giraldo, A parameter-free dynamic alternative to hyper-viscosity for coupled transport equations: applications to the simulation of 3D squall lines using spectral elements, Journal of Computational Physics, Vol. 283, 360-373 (2015) (ResearchGate).
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S. Marras, M.A. Kopera and F.X. Giraldo, Simulation of shallow water jets with a unified element-based continuous/discontinuous Galerkin model with grid flexibility on the sphere, Quarterly Journal of the Royal Meteorological Society, Vol. 141, 1727-1739 (2015) (ResearchGate).
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2014
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W. Kang, L. Xu, F.X. Giraldo, Partial observability and its consistency for PDEs (unpublished) (2014) (ResearchGate) (arXiv).
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S.J. Choi, F.X. Giraldo, J. Kim, and S. Shin, Verification of a non-hydrostatic dynamical core using horizontally spectral element and vertically finite difference methods: 2D aspects, Geoscientific Model Development, Vol. 7, 2717-2731 (2014) (ResearchGate).
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S.J. Choi and F.X. Giraldo, Development and evaluation of a hydrostatic dynamical core using the spectral element/discontinuous Galerkin methods, Geoscientific Model Development, Vol. 7, 4119-4151 (2014) (ResearchGate).
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M.A. Kopera and F.X. Giraldo, Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations, Journal of Computational Physics Vol. 275, 92-117 (2014) (ResearchGate).
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L. Yelash, A. Mueller, M. Lukacova-Medvidova, F.X. Giraldo, V. Wirth, Adaptive discontinuous evolution Galerkin method for dry atmospheric flow, Journal of Computational Physics Vol. 268 106-133 (2014) (ResearchGate).
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S. Marras, A. Mueller, and F.X. Giraldo, Physics-based stabilization of spectral elements for the 3D Euler equations of moist atmospheric convection, Proceedings of ICOSAHOM, DOI: 10.1007/978-3-319-19800-2_32, June (2014) (ResearchGate).
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2013
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F.X. Giraldo, J.F. Kelly and E.M. Constantinescu, Implicit-Explicit formulations for a 3D nonhydrostatic unified model of the atmosphere (NUMA), SIAM J. Sci. Comp., Vol. 35 (5), B1162-B1194 (2013) (ResearchGate).
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A. Mueller, J. Behrens, F.X. Giraldo, and V. Wirth, Comparison between adaptive and uniform discontinuous Galerkin simulations in 2D dry bubble experiments, J. Comp. Phys., Vol. 235, 371-393 (2013) (ResearchGate).
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F.X. Giraldo, Continuous and Discontinuous Galerkin Methods for Atmospheric Modeling, Proceedings of ECMWF Workshop: Recent Developments in Numerical Methods for Atmosphere and Ocean Modeling (2013) (PDF).
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2012
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Marras, J.F. Kelly, F.X. Giraldo, and M. Vazquez, Variational multiscale stabilization and p-adaptivity of high-order spectral elements for the convection-diffusion equation, J. Comp. Phys., Vol. 231, 7187-7213 (2012) (ResearchGate).
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J.F. Kelly and F.X. Giraldo, Continuous and discontinuous Galerkin methods for a scalable 3D nonhydrostatic atmospheric model: limited-area mode, J. Comp. Phys., Vol. 231, 7988-8008 (2012) (ResearchGate).
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S. Gabersek, F.X. Giraldo, and J. Doyle, Dry and moist idealized experiments with a two-dimensional spectral element model, Mon. Wea. Rev., Vol. 140, 3163-3182 (2012) (ResearchGate).
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L.E. Carr, C.F. Borges, and F.X. Giraldo, An element-based spectrally-optimized approximate inverse preconditioner for the Euler equations, SIAM J. Sci. Comp., Vol. 34, B392-B420 (2012) (ResearchGate).
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J. Lindquist, B. Neta, and F.X. Giraldo, High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements, Appl. Maths. Comp., Vol. 218, 6666-6676 (2012) (ResearchGate).
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J.A. Escobar-Vargas, P.J. Diamessis, F.X. Giraldo, High-order discontinuous element-based schemes for the inviscid shallow water equations: spectral multidomain penalty and discontinuous Galerkin methods, Appl. Maths. Comp., Vol. 218, 4825-4848 (2012) (ResearchGate).
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2010
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F.X. Giraldo, M. Restelli, and M. Laeuter, Semi-implicit formulations of the Euler equations: applications to nonhydrostatic atmospheric modeling, SIAM J. Sci. Comp., Vol. 32, 3394-3425 (2010) (ResearchGate).
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J. Lindquist, F.X. Giraldo, and B. Neta, Klein-Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions, Appl. Maths. Comp., Vol. 217, 2710-2723 (2010) (ResearchGate).
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J. Lindquist, B. Neta, and F.X. Giraldo, A spectral element solution of the Klein-Gordon equation with high-order non-reflecting boundary conditions, Wave Motion, Vol. 47, 289-298 (2010) (ResearchGate).
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Matthias Laeuter, Francis X. Giraldo, Sebastian Reich, Marco Restelli, Doerthe Handorf, Klaus Dethloff, A 2D Unified (Non-) Hydrostatic Model of the Atmosphere with a Discontinuous Galerkin Method (unpublished 2010) (PDF).
2009
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F.X. Giraldo and M. Restelli, High-Order Semi-Implicit Time-Integration of a Triangular Discontinuous Galerkin Oceanic Shallow Water Model, Int. J. Num. Meths. Fluids, Vol. 63, 1077-1102 (2009) (ResearchGate).
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J.R. Dea, F.X. Giraldo, and B. Neta, High-Order Non-Reflecting Boundary Conditions for the Linearized 2D Euler Equations: No Mean Flow, Wave Motion, Vol. 46, 210-220 (2009) (ResearchGate).
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M. Restelli and F.X. Giraldo, A Conservative Semi-Implicit Discontinuous Galerkin Method for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Atmospheric Modeling, SIAM J. Sci. Comp., Vol. 31, 2231-2257 (2009) (ResearchGate).
2008
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M. Laueter, F.X. Giraldo, D. Hansdorf, and K. Dethloff, A Discontinuous Galerkin Method for the Shallow Water Equations with Spherical Triangular Coordinates, J. Comp. Phys., Vol. 227, 10226-10242 (2008) (ResearchGate).
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Y.J. Kim, F.X. Giraldo, M. Flatau, C.S. Liou, and M.S. Peng, A Sensitivity Study of the Kelvin Wave and the Madden-Julian Oscillation in Aqua-planet Simulations by the Naval Research Laboratory Spectral Element Atmospheric Model (NSEAM), J. Geophys. Res., Vol. 113 (2008) (ResearchGate).
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F.X. Giraldo and M. Restelli, A Study of Spectral Element and Discontinuous Galerkin Methods for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Atmospheric Modeling: Equation Sets and Test Cases, J. Comp. Phys., Vol. 227, 3849-3877 (2008) (ResearchGate).
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F.X. Giraldo and T. Warburton, A High-Order Triangular Discontinuous Oceanic Shallow Water Model, Int. J. Num. Meths. Fluids, Vol. 56, 899-925 (2008) (ResearchGate).
2006
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F.X. Giraldo, Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators, Comp. Maths. Appls., Vol. 52, 1325-1342 (2006) (ResearchGate).
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F.X. Giraldo and M.A. Taylor, A Diagonal Mass Matrix Triangular Spectral Element Method based on Cubature Points, J. of Eng. Maths., Vol. 56, 307-322 (2006) (ResearchGate).
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F.X. Giraldo, High-order Triangle-based Discontinuous Galerkin Methods for Hyperbolic Equations on a Rotating Sphere, J. Comp. Phys., Vol. 214, 447-465 (2006) (ResearchGate).
2005
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F.X. Giraldo and T. Warburton, A Nodal Triangle-based Spectral Element Method for the Shallow Water Equations on the Sphere, J. Comp. Phys., Vol. 207, 129-150 (2005) (ResearchGate).
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F.X. Giraldo, Semi-implicit Time-Integrators for a Scalable Spectral Element Atmospheric Model, Quart. J. Roy. Meteor. Soc., Vol. 131, 2431-2454 (2005) (ResearchGate).
2004
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F.X. Giraldo and T. Rosmond, A Scalable Spectral Element Eulerian Atmospheric Model (SEE-AM) for NWP: Dynamical Core Tests, Mon. Wea. Rev., Vol.132, 133-153 (2004) (ResearchGate).
2003
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F.X. Giraldo, J.B. Perot, and P.F. Fischer, A Spectral Element Semi-Lagrangian (SESL) Method for the Spherical Shallow Water Equations, J. Comp. Phys., Vol.190, 623-650 (2003) (ResearchGate).
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F.X. Giraldo, Strong and Weak Lagrange-Galerkin Spectral Element Methods for the Shallow Water Equations, Comp. Maths. Appls. Vol. 45, 97-121 (2003) (ResearchGate).
2002
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F.X. Giraldo, J.S. Hesthaven, and T. Warburton, Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations, J. Comp. Phys., Vol. 181, 499-525 (2002) (ResearchGate).
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W. Chang, F.X. Giraldo, and J.B. Perot, Analysis of an Exact Fractional-Step Method, J. Comp. Phys., Vol. 180, 183-1995 (2002) (ResearchGate).
2001
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F.X. Giraldo, A Spectral Element Shallow Water Model on Spherical Geodesic Grids, Int. J. Num. Meths. Fluids, Vol. 35, 869-901 (2001) (ResearchGate).
2000
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F.X. Giraldo, The Lagrange-Galerkin Method for the 2D Shallow Water Equations on Adaptive Grids, Int. J. Num. Meths. Fluids, Vol. 33, 789-832 (2000) (ResearchGate).
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F.X. Giraldo, Lagrange-Galerkin Methods on Spherical Geodesic Grids: The Shallow Water Equations, J. Comp. Phys., Vol. 160, 336-368 (2000) (ResearchGate).
1999
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F.X. Giraldo, Trajectory Calculations for Spherical Geodesic Grids in Cartesian Space, Mon. Wea. Rev., Vol. 127, 1651-1662 (1999) (ResearchGate).
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F.X. Giraldo and B. Neta, Stability Analysis for Eulerian and Semi-Lagrangian Finite Element Formulation of the Advection-Diffusion Equation, Comp. Maths. Appls., Vol. 38, 97-112 (1999).
1998
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F.X. Giraldo, The Lagrange-Galerkin Spectral Element Method on Unstructured Quadrilateral Grids, J. Comp. Phys., Vol. 147, 114-146 (1998) (ResearchGate).
1997
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F.X. Giraldo, Lagrange-Galerkin Methods on Spherical Geodesic Grids, J. Comp. Phys., Vol. 136, 197-213 (1997) (ResearchGate).
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B. Neta, F.X. Giraldo, and I.M. Navon, Analysis of the Turkel-Zwas scheme for the Two-Dimensional Shallow Water Equations in Spherical Coordinates, J. Comp. Phys., Vol. 133, 102-122 (1997) (ResearchGate).