David Gardner is a computational scientist in the Scientific Computing group within the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory (LLNL). His work focuses on the development and implementation of accurate and efficient time integration methods and nonlinear solvers for simulating multi-scale, multi-physics problems on high performance computing systems. As part of the Exascale Computing Project and FASTMath SciDAC Institute David contributes to the SUNDIALS suite of time integrators and nonlinear solvers.

In prior projects David has worked on the Energy Exascale Earth System Model (E3SM) to improve the numerical convergence of atmospheric physics processes, evaluate the accuracy and efficiency of implicit-explicit time integrators for non-hydrostatic atmospheric dynamics, design and implement preconditioners for fully implicit integration methods for hydrostatic atmospheric dynamics, and develop time integrators for coupled atmospheric physics processes. David has also worked on fully implicit time integration methods and nonlinear solvers for dislocation dynamics in the Parallel Dislocation Simulator (ParaDiS) and filtering methods for noisy data in hybrid continuum-atomistic simulations.

David joined CASC in July 2014 as a postdoctoral researcher after completing his Ph.D. in Computational and Applied Mathematics at Southern Methodist University (SMU).

ResearcherID: T-4094-2017

ORCID: 0000-0002-7993-8282

**Refereed Publications**

- D. J. Gardner, J. E. Guerra, F. P. Hamon, D. R. Reynolds, P. A. Ullrich, and C. S. Woodward, "Implicit-explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models,"
*Geoscientific Model Development*, 11, 1497-1515, 2018. [DOI] - K. J. Evans, R. K. Archibald, D. J. Gardner, M. R. Norman, M. A. Taylor, C. S. Woodward, and P. A. Worley, "Performance analysis of fully explicit and fully implicit solvers within a spectral element shallow-water atmosphere model,"
*The International Journal of High Performance Computing Applications*, 2017. [DOI] - D. J. Gardner and D. R. Reynolds, "Filters for improvement of multiscale data from atomistic simulations,"
*Multiscale Modeling & Simulation*, 15:1, 1-28, 2017. [DOI] - D. J. Gardner, C. S. Woodward, D. R. Reynolds, G. Hommes, S. Aubry, and A. Arsenlis, "Implicit integration methods for dislocation dynamics,"
*Modelling and Simulation in Materials Science and Engineering*, 23:025006, 2015. [DOI] - C. S. Woodward, D. J. Gardner, and K. J. Evans, "On the Use of Finite Difference Matrix-Vector Products in Newton-Krylov Solvers for Implicit Climate Dynamics with Spectral Elements,"
*Procedia Computer Science*, 51:2036-2045, 2015. [DOI]

**Invited Presentations**

- D. J. Gardner, C. S. Woodward, D. R. Reynolds, A. C. Hindmarsh, and C. J. Balos,
*Multirate Integrators in SUNDIALS*, International Conference on Scientific Computation and Differential Equations, University of Innsbruck, Innsbruck, Austria, July 22 – 26, 2019. - D. J. Gardner, P. Rasch, P. Stinis, C. J. Vogl, H. Wan, C. S. Woodward, S. Zhang,
*Assessing and Improving the Numerical Solution of Atmospheric Physics in E3SM*, SIAM Conference on Mathematical & Computational Issues in the Geosciences, Houston, TX, March 11 – 14, 2019. - D. J. Gardner, C. S. Woodward, D. R. Reynolds, A. C. Hindmarsh, S. Peles, and C. J. Balos,
*The SUNDIALS Suite of Time Integrators and Nonlinear Solvers: Preparing for Exascale Computing*, SIAM Conference on Computational Science and Engineering, Spokane, WA, Feburary 25 – March 1, 2019. - D. J. Gardner, C. S. Woodward, H. Wan, C. J. Vogl, and P. Rasch,
*Assessing and Improving the Numerical Solution of Atmospheric Physics in E3SM*, SIAM Conference on the Mathematics of Planted Earth, Philadelphia, PA, September 13 – 15, 2018. - D. J. Gardner, C. S. Woodward, D. R. Reynolds, A. C. Hindmarsh, S. Peles, J. Loffeld, and C. J. Balos,
*The SUNDIALS Suite of Time Integrators and Nonlinear Solvers*, Bout++ Workshop, Livermore, CA, August 14 – 17, 2018. - D. J. Gardner, C. S. Woodward, D. R. Reynolds, A. C. Hindmarsh, and S. Peles,
*SUNDIALS Suite of Time Integrators and Nonlinear Solvers*(poster), SIAM Annual Meeting, Portland, OR, July 9 – 13, 2018. - D. J. Gardner, J. E. Guerra, F. P. Hamon, D. R. Reynolds, P. A. Ullrich, and C. S. Woodward,
*Implicit-Explicit Time Integration Methods for Non-hydrostatic Atmospheric Models*, IMAGe 2017 Theme of the Year: Workshop on Multiscale Geoscience Numerics, NCAR Mesa Lab, Boulder, CO, May 16 – 19, 2017. - D. J. Gardner, J. E. Guerra, F. P. Hamon, D. R. Reynolds, P. A. Ullrich, and C. S. Woodward,
*Implicit-Explicit Time Integration Methods for Non-hydrostatic Atmospheric Models*, SIAM Conference on Mathematics of Planet Earth, Philadelphia, PA, September 30 – October 2, 2016. - D. J. Gardner, C. S. Woodward, P. M. Caldwell, and K. J. Evans,
*Advanced Time Integration Methods for Atmospheric Physics*(poster), AXICCS Workshop, Rockville, MD, September 12 – 13, 2016. - D. J. Gardner, R. Archibald, K. J. Evans, P. A. Ullrich, C. S. Woodward, and P. H. Worley,
*Scalable Nonlinear Solvers and Preconditioners in Climate Applications*, SIAM Conference on Parallel Processing for Scientific Computing, Paris, France, April 12 – 15, 2016. - D. J. Gardner, C. S. Woodward, D. R. Reynolds, K. Mohror, G. Hommes, S. Aubry, M. Rhee, and A. Arsenlis,
*Implicit Integration Methods for Dislocation Dynamics,*Numerical Methods for Large-Scale Nonlinear Problems and Their Applications, ICERM, Providence, RI, August 31 – September 4, 2015. - D. J. Gardner, P. M. Caldwell, J. M. Sexton, and C. S. Woodward,
*Numerical Errors in Coupling Micro and Macrophysics in the Community Atmosphere Model*, SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, Stanford, CA, June 29 – July 2, 2015. - D. J. Gardner, K. J. Evans, P. A. Lott, A. Salinger, and C. S. Woodward,
*Preconditioners for Implicit Atmospheric Climate Simulations in the Community Atmosphere Model*, SIAM Conference on Computational Science and Engineering, Salt Lake City, UT, March 14 – 18, 2015.

**Presentations**

- D. J. Gardner, C. S. Woodward, D. R. Reynolds, A. C. Hindmarsh, and C. J. Balos,
*The SUNDIALS Suite of Nonlinear and Differential / Algebraic Equation Solvers*(poster), International Congress on Industrial and Applied Mathematics, Valencia, Spain, July 15 – 19, 2019. - D. J. Gardner and D.R. Reynolds,
*Improving the Computational Efficiency of Multiscale Simulations with Filtering*, SIAM Conference on Computational Science and Engineering, Atlanta, GA, February 27 – March 3, 2017. - D. J. Gardner, J. E. Guerra, F. P. Hamon, D. R. Reynolds, P. A. Ullrich, and C. S. Woodward,
*Implicit-Explicit Time Integration Methods for Non-hydrostatic Atmospheric Models*(poster)*,*AGU Fall Meeting, San Francisco, CA, December 12 – 16, 2016. - D. J. Gardner and D. R. Reynolds,
*Filters for the Improvement of Multiscale Data from Atomistic Simulations*, SIAM Annual Meeting, Boston, MA, July 11 – 15, 2016. - D. J. Gardner, P. M. Caldwell, and C. S. Woodward,
*Advanced Time Integration Methods for Atmospheric Physics*(poster), SIAM Annual Meeting, Boston, MA, July 11 – 15, 2016. - D. J. Gardner and D. R. Reynolds,
*Filters for the Improvement of Multiscale Data from Atomistic Simulations*(poster), SIAM Conference on Parallel Processing for Scientific Computing, Paris, France, April 12 – 15, 2016. - D. J. Gardner, R. Archibald, K. J. Evans, and C. S. Woodward,
*Implicit Time Stepping and Preconditioning for Global Atmospheric Dynamics in Climate Simulation*, Fourteenth Copper Mountain Conference on Iterative Methods, Copper Mountain, CO, March 20 – 25, 2016. - D. J. Gardner, K. J. Evans, C. S. Woodward, R. Archibald, and P. H. Worley,
*Implicit Time Stepping and Preconditioning for Atmospheric Dynamics in the Community Atmosphere Model*(poster), AGU Fall Meeting, San Francisco, CA, December 14 – 18, 2015. - C. S. Woodward, D. R. Reynolds, A. C. Hindmarsh, L. E. Banks, and D. J. Gardner,
*SUNDIALS: Suite of Nonlinear and Differential / Algebraic equation solvers*(poster), 2015 Scientific Discovery through Advanced Computing (SciDAC-3) Principal Investigator Meeting, Bethesda, MD, July 22 – 24, 2015. - D. J. Gardner, P. M. Caldwell, J. M. Sexton, and C. S. Woodward,
*Numerical Errors in Coupling Micro- and Macrophysics in the Community Atmosphere Model*(poster), AGU Fall Meeting, San Francisco, CA, December 15 – 19, 2014.