Carol S. Woodward


Portrait of  Carol S. Woodward
  • Title
    Distinguished Member of the Technical Staff
  • Email
  • Phone
    (925) 424-6013
  • Organization

Dr. Carol Woodward is a Distinguished Member of the Technical Staff at Lawrence Livermore National Laboratory.  Her research interests include numerical methods for nonlinear partial differential equations, nonlinear and linear solvers, time integration methods, numerical software development, and parallel computing. She leads the development and deployment of the SUNDIALS package of time integrators and nonlinear solvers which garners over 100,000 downloads/clones each year. SUNDIALS is a part of the Exascale Computing Project and the FASTMath SciDAC Institute. Dr. Woodward also participates in an earth system SciDAC partnership project on assessing and improving numerical convergence in atmospheric physics and in a SciDAC partnership on non-equilibrium quantum dynamical system simulations.

Dr. Woodward serves on the editorial board for ACM Transactions on Mathematical Software and has served on numerous organizing committees for national and international meetings. She currently serves as the ICIAM (International Council on Industrial and Applied Mathematics) representative on the Standing Committee for Gender Equality in Science, an international committee of scientific professional unions formed to promote gender equality in sciences worldwide. Dr. Woodward was named to the 2017 Class of Fellows of the Society for Industrial and Applied Mathematics and to the 2021 Class of Fellows of the Association for Women in Mathematics. In 2015 Dr. Woodward was one of 15 early- and mid-career scientists and engineers recognized by LLNL for exceptional technical achievement.

Dr. Woodward will start a term as President-Elect  of the Society for Industrial and Applied Mathematics (SIAM) in 2024 and serve as its President in 2025-2026.  She served as Vice President-at-Large of SIAM 2018–2021. In addition, she served as Numerical Methods Group Leader and Postdoctoral Program Manager in the LLNL Center for Applied Scientific Computing, four years as an At-Large Member of the Association for Women in Mathematics Executive Committee, and six years as an elected member of the SIAM Council. She has also held offices in the SIAM activity groups on Geosciences and Computational Science and Engineering and was the SIAM representative to the Joint Committee on Women in the Mathematical Sciences for three years (two as Committee Chair).

Dr. Carol Woodward has been a computational mathematician in the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory (LLNL) since June of 1996. Prior to that time, she attended Rice University where she received a PhD in Computational and Applied Mathematics and Louisiana State University where she graduated with a B.S. in Mathematics. She completed high school at the Louisiana School for Math, Science and Arts, a two year residential high school that emphasizes advanced study in mathematics, sciences, humanities, and arts.

A position paper Woodward wrote with colleague, Jeff Hittinger, discussing some of the things DOE labs look for in trained computational scientists can be found on the Computing website.

For other information, see

For ORC ID information, see:

Refereed Journal and Conference Papers

  1. Vogl CJ, Wan H, Woodward CS, Bui QM. Numerical coupling of aerosol emissions, dry removal, and turbulent mixing in the E3SM Atmosphere Model version 1 (EAMv1), part II: a semi-discrete error analysis framework for assessing coupling schemes. arXiv preprint arXiv:2306.04929. 2023. To appear in Geoscience Model Development.
  2. John J. Loffeld and Andy Nonaka and Daniel R. Reynolds and David J. Gardner and Carol S. Woodward, “Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks,” To appear in Int. J. High Perf. Comput. Appl.
  3. Zhang S, Vogl CJ, Larson VE, Bui QM, Wan H, Rasch PJ, Woodward CS. Removing numerical pathologies in a turbulence parameterization through convergence testing. Journal of Advances in Modeling Earth Systems. 2023 May;15(5):e2023MS003633.
  4. Reynolds, Daniel R. and Gardner, David J. and Woodward, Carol S. and Chinomona, Rujeko, 2023. ARKODE: A Flexible IVP Solver Infrastructure for One-Step Methods. ACM Trans Math Softw. volume 49, issue 2, pp. 1–26, 2023,
  5. Gardner, D. J., Reynolds, D.R., Woodward, C.S., and Balos, C. J., "Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers," ACM Trans. on Math. Software, Vol. 48, No. 3, Sept. 2022.
  6. Lockhart S, Gardner DJ, Woodward CS, Thomas S, Olson LN. Performance of Low Synchronization Orthogonalization Methods in Anderson Accelerated Fixed Point Solvers. Proceedings of SIAM Conference on Parallel Computing, 2022, pp. 49-59.
  7. Balos CJ, Gardner DJ, Woodward CS, Reynolds DR. “Enabling GPU Accelerated Computing in the SUNDIALS Time Integration Library,” Parallel Computing, 108, Dec. 2021.
  8. I. Aggarwal, A. Kashi, P. Nayak, C. J. Balos, C. S. Woodward and H. Anzt, "Batched Sparse Iterative Solvers for Computational Chemistry Simulations on GPUs," 2021 12th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA), 2021, pp. 35-43,
  9. Roberts S, Loffeld J, Sarshar A, Woodward CS, Sandu A., “Implicit multirate GARK methods,” Journal of Scientific Computing 87.1 (2021): 1-32.
  10. C. Vogl, S. Zhang, C. Woodward, H. Wan, P. Stinis, “Improving Time Step Convergence in an Atmosphere Model With Simplified Physics: Using Mathematical Rigor to Avoid Nonphysical Behavior in a Parameterization." Journal of Advances in Modeling Earth Systems. 2020 Oct;12(10):e2019MS001974.
  11. H. Wan, C. Woodward, S. Zhang, C. Vogl, P. Stinis, D. Gardner, P. Rasch, X. Zeng, V. Larsen, and B. Singh, “Improving Time Step Convergence in an Atmosphere Model With Simplified Physics: The Impacts of Closure Assumption and Process Coupling." Journal of Advances in Modeling Earth Systems. 2020 Oct;12(10):e2019MS001982.
  12. S. Guenther, R. D. Falgout, P. Top, C. S. Woodward, and J. Schroder, “Parallel-in-Time Solution of Power Systems with Unscheduled Events,” proceedings of the 2020 IEEE Power and Energy Society General Meeting (PESGM).
  13. B. Kuffuor, N. Engdahl, C. Woodward, L. Condon, S. Kollet, and R. Maxwell, “Simulating Coupled Surface-Subsurface Flows with ParFlow v3.5.0: Capabilities, applications, and ongoing development of an open-source, massively parallel, integrated hydrologic model,” Geoscientific Model Development, 13(3), 1373-1397, 10.5194/gmd-13-1373-2020, 2020.
  14. M. Lecouvez, R. D. Falgout, and C. S. Woodward, “A parallel-in-time algorithm for variable step multistep methods,” Journal of Computational Science37, p.101029, 2019.
  15. Vogl, Christopher J., Andrew Steyer, Daniel R. Reynolds, Paul A. Ullrich, and Carol S. Woodward. "Evaluation of Implicit-Explicit Additive Runge-Kudda Integrators for the HOMME-NH Dynamical Core." Journal of Advances in Modeling Earth Systems, 11(12), p.4228-4244,, 2019.
  16. S. Zhang, H. Wan, P. Rasch, B. Singh, V. Larsen, and C. Woodward, “An objective and efficient method for assessing the impact of reduced-precision calculations on solution correctness,” Journal of Advances in Modeling Earth Systems, 11, 3131-3147., 2019.
  17. I. Karlan, Y. Park, B. de Supinski, P. Wang, B. Still, D. Beckinsale, R. Blake, T. Chen, G. Cong, C. Costa, J. Dahm, G. Domeniconi, T. Epperly, A. Fisher, S. Schumacher, S. Langer, H. Le, E. Lee, N. Maruyama, X. Que, D. Richards, B. Sjogreen, J. Wong, C. Woodward, U. Yang, X. Zhang, et al., “Preparation and Optimization of a Diverse Workload for a Large-Scale Heterogeneous System,” In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, p. 32. ACM, 2019.
  18. J. B. Schroder, M. Lecouvez, R. D. Falgout, C. S. Woodward, and P. Top, "Parallel-in-Time Solution of Power Systems with Scheduled Events," IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5, IEEE, 2018.
  19. Gardner, D. J., Guerra, J. E., Hamon, F. P., Reynolds, D. R., Ullrich, P. A., and Woodward, C. S., "Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models," Geosci. Model Dev., 11, 1497-1515,, 2018.
  20. K. J. Evans, R. K. Archibald, D. J. Gardner, M. R. Norman, M. A. Taylor, C. S. Woodward, and P. H. Worley, “Performance analysis of fully explicit and fully-implicit solvers within a spectral-element shallow-water atmosphere model,” International Journal of High Performance Computing Applications, DOI: 10.1177/109434201773637
  21. J. Loffeld and C. S. Woodward, "Considerations on the implementation and use of Anderson acceleration on distributed memory and GPU-based parallel computers," in Letzter, Gail, et al., eds. Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium. Vol. 6. Springer, 2016.
  22. W. Collins, K. J. Evans, H. Johansen, C. S. Woodward, and P. Caldwell, “Progress in Fast, Accurate Multi-scale Climate Simulations,” Procedia Computer Science, 51, (2015), pp. 2006-2015.  DOI: 10.1016/j.procs.2015.05.465.
  23. Lecouvez, Matthieu, Robert D. Falgout, Carol S. Woodward, and Philip Top. "A parallel multigrid reduction in time method for power systems." In Power and Energy Society General Meeting (PESGM), pp. 1-5. IEEE, 2016.
  24. Wilson, Anastasia, Wei Du, Guanglian Li, Azam Moosavi, and Carol S. Woodward. "On Metrics for Computation of Strength of Coupling in Multiphysics Simulations." In Topics in Numerical Partial Differential Equations and Scientific Computing, pp. 137-176. Springer New York, 2016.
  25. 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, (2015), pp. 2036-2045.  DOI: 10.1016/j.procs.2015.05.468.
  26. P. A. Lott, C. S. Woodward, and K. J. Evans, “Algorithmically Scalable Block Preconditioner for Fully Implicit Shallow-Water Equations in CAM-SE,” Computational Geosciences, 19(1), 2015, pp. 49-61.  DOI: 10.1007/s10596-014-9447-6.
  27. B. M. Kelley, P. Top, S. G. Smith, C. S. Woodward, and L. Min, “A Federated Simulation Toolkit for Electric Power Grid and Communication Network Co-simulation,” in refereed proceedings of 2015 Workshop on Modeling and Simulation of Cyber-Physical Energy Systems (MSCPES), Seattle, WA, April 2015.
  28. 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(2):025006, 2015.
  29. D. Osei-Kuffuor, R. M. Maxwell, and C. S. Woodward, “Methods for Implicit Coupling of Subsurface and Overland Flow,” Advances in Water Resources, 74 (2014), pp 185–195.  DOI: 10.1016/j.advwatres.2014.09.006.
  30. S. Smith, C. Woodward, L. Min, C. Jing, A. Del Rosso, “On-Line Transient Stability Analysis using High Performance Computing,” in  Innovative Smart Grid Technologies Conference (ISGT), 2014 IEEE PES, Feb. 2014.  DOI: 10.1109/ISGT.2014.6816438.
  31. J. M. Connors, J. W. Banks, J. A. F. Hittinger, C. S. Woodward, “Quantification of Errors for Operator-Split Advection-Diffusion Calculations,” Computer Methods in Applied Mechanics and Engineering, Vol. 272, pp. 181-197, Apr., 2014.  DOI: 10.1016/j.cma.2014.01.005.
  32. J. M. Connors, J. W. Banks, J. A. F. Hittinger and C. S. Woodward, “A method to calculate numerical errors using adjoint error estimation for linear advection,” SIAM J. Numer. Anal. 51(2),  2013, pp. 894-926.  DOI: 10.1137/110845100.
  33. J. W. Banks, J. A. F. Hittinger, J. M. Connors, C. S. Woodward, “A Posteriori error estimation via nonlinear error transport with application to shallow water,” in Recent Advances in Scientific Computing and Applications, Contemporary Mathematics, 586, Amer. Math. Soc., Providence, RI, 2013, pp. 35-42.  DOI: 10.1090/conm/586/11646.
  34. D. E. Keyes, L. C. McInnes, C. Woodward, W. D. Gropp, E. Myra, M. Pernice, J. Bell, J. Brown, A. Clo, J. Connors, E. Constantinescu, D. Estep, K. Evans, C. Farhat, A. Hakim, G. Hammond, G. Hansen, J. Hill, T. Isaac, X. Jiao, K. Jordan, D. Kaushik, E. Kaxiras, A. Koniges, K. Lee, A. Lott, Q. Lu, J. Magerlein, R. Maxwell, M. McCourt, M. Mehl, R. Pawlowski, A. P. Randles, D. Reynolds, B. Riviere, U. Rüde, T. Scheibe, J. Shadid, B. Sheehan, M. Shephard, A. Siegel, B. Smith, X. Tang, C. Wilson, and B. Wohlmuth, “Multiphysics simulations: Challenges and opportunities,” International Journal of High Performance Computing Applications 27, pp. 4–83, 2013.  DOI: 10.1177/1094342012468181.
  35. Lott, P.A., H.F. Walker, C.S. Woodward, U.M. Yang, “An accelerated Picard method for nonlinear systems related to variably saturated flow,” Adv. Wat. Resour., 38 (2012), pp. 92-101.  DOI: 10.1016/j.advwatres.2011.12.013.
  36. J. W. Banks, J. A. Hittinger, J. M. Connors and C. S. Woodward, “Numerical error estimation for nonlinear hyperbolic PDEs via nonlinear error transport,” Computer Methods in Applied Mechanics and Engineering, 213, pp. 1-15, 2012.  DOI: 10.1016/j.cma.2011.11.021.
  37. Reed M. Maxwell, Julie K. Lundquist, Jeff Mirocha, Steven G. Smith, Carol S. Woodward, and Andrew F.B. Tompson, “Development of a coupled groundwater-atmospheric model,” Monthly Weather Review, 139(1), 2011,  pp.  96–116.  DOI: 10.1175/2010MWR3392.1.
  38. Kollet S., Maxwell R., Woodward C.S., et al., “Proof-of-concept of regional scale hydrologic simulations at hydrologic resolution utilizing massively parallel computer resources,” Water Resour. Res., 46, 2010, W04201, doi:10.1029/2009WR008730, 1-7.  Featured Article with Water Resources Research (given to only 5% of accepted papers).
  39. Reynolds, D.R., R. Samtaney, and C.S. Woodward, “Operator-Based Preconditioning of Stiff Hyperbolic Systems,” SIAM J. on Sci. Comp., 32(1), pp. 150-170, 2010.  DOI: 10.1137/080713331.
  40. Reynolds, D.R., Swesty, D.O., and Woodward, C.S., “A Newton-Krylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae,” 2008 J. Phys.: Conf. Ser. 125 012085.  DOI: 10.1088/1742-6596/125/1/012085. 
  41. Brown, P. N., H. F. Walker, R. Wasyk, and C. S. Woodward, “On using approximate finite-differences in matrix-free Newton--Krylov methods,” SIAM J. Numer. Anal., 46 (2007), pp. 1892–1911.  DOI: 10.1137/060652749.
  42. D. R. Reynolds, R. Samtaney and C. S. Woodward, “A fully implicit numerical method for single-fluid resistive magnetohydrodynamics,” Journal of Computational Physics219(1), (2006), pp 144-162.  DOI: 10.1016/
  43. D. E. Keyes, D. R. Reynolds and C. S. Woodward, "Implicit solvers for large-scale nonlinear problems," Journal of Physics:
    Conference Series
    , 46:433-442, 2006. DOI: 10.1088/1742-6596/46/1/060.
  44. A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. Shumaker, and C. S. Woodward, “SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers,” ACM Transactions on Mathematical Software, 31(3), (2005), pp. 363 - 396. DOI: 10.1145/1089014.1089020. 
  45. Brown Peter N., Dana E. Shumaker, and Carol S. Woodward, “Fully Implicit Solution of Large-Scale Non-Equilibrium Radiation Diffusion with High Order Time Integration,” J. Comp. Phys., 204(2), (2005), pp. 760-783.  DOI: 10.1016/
  46. Lee, S. L., C. S. Woodward, and F. R. Graziani, “Analyzing Radiation Diffusion Using Time-Dependent Sensitivity-Based Techniques,” Journal of Computational Physics, 192, (1), (2003), pp. 211-230. DOI: 10.1016/
  47. Brown, P. N., P. Vassilevski, and C. S. Woodward, “On Mesh-Independent Convergence of an Inexact Newton-Multigrid Algorithm,” SIAM J. Sci. Comput., 25, (2), (2003), pp. 570-590.  DOI: 10.1137/S1064827502407822.
  48. Brown, P.N., and C.S. Woodward, “Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer,” SIAM J. Sci. Comput., 23, (2), (2001), pp. 499-516.  DOI: 10.1137/S106482750037295X.
  49. Jones, J.E., and C.S. Woodward, “Newton-Krylov-Multigrid Solvers for Large-Scale, Highly Heterogeneous, Variably Saturated Flow Problems,” Adv. Water Resources, 24, (July 2001), pp. 763-774.  DOI: 10.1016/S0309-1708(00)00075-0.
  50. Woodward, C.S., and C. N. Dawson, “Analysis of Expanded Mixed Finite Element Methods for a Nonlinear Parabolic Equation Modeling Flow into Variably Saturated Porous Media,” SIAM J. Numerical Analysis, 37, (3, 2000), 701-724.  DOI: 10.1137/S0036142996311040.
  51. Dawson, C.N., M.F. Wheeler, and C.S. Woodward, “A Two-Grid Finite Difference Scheme for Nonlinear Parabolic Equations,” SIAM J. Numerical Analysis, 35, (2/1998).  DOI: 10.1137/S0036142995293493.
  52. Dawson, C.N., H. Klie, M.F. Wheeler, and C.S. Woodward, “A Parallel, Implicit, Cell-Centered Method for Two-Phase Flow with a Preconditioned Newton–Krylov Solver,” Computational Geosciences, 1, (3/4,1997), 215–249.
  53. Gray, L.J., and C. San Soucie (Woodward), “A Hermite Interpolation Algorithm for Hypersingular Boundary Integrals,” International Journal for Numerical Methods in Engineering, 36, (1993), pp. 2357–2367. DOI: 10.1002/nme.1620361404.

Unrefereed Conference Papers and Book Chapters

  1. P. A. Lott, H. C. Elman, K. J. Evans, X. S. Li, A. G. Salinger, and C. S. Woodward, “Recent Progress in Nonlinear and Linear Solvers,” in Proc. SciDAC 2011, Denver, CO, July 10-14, 2011,
  2. C.S. Woodward and J.A.F. Hittinger, “Numerical Convergence Studies of Weapon Calculations,” Proceedings of the 2010 NECDC, Los Alamos, NM, Oct. 2010.
  3. Walker, H.F., C.S. Woodward, and U.M. Yang, “An Accelerated Fixed-Point Iteration for Solution of Variably Saturated Flow,” in Proceedings of the XVIII International Conference on Computational Methods in Water Resources (CMWR 2010), J. Carrera, X. Sanchez Villa, D. Fernandez Garcia, et al. eds., Int. Center for Numerical Methods in Engineering, Barcelona, Spain, pp. 216-223, 2010.
  4. Anderson, S., B. Bihari, K. Salari, and C. S. Woodward, “Code Verification Results of an LLNL ASC Code on Some Tri-Lab Verification Test Suite Problems,”  proceedings of the NECDC 2006.
  5. Shumaker, Dana E. and Carol S. Woodward, “Implicit Solution of Non-Equilibrium Radiation Diffusion Including Reactive Heating Source in Material Energy Equation,” in “Computational Methods in Transport,” F. Graziani, ed., Springer, Berlin, (2006), pp. 353-370.
  6. Miller, D.S. and C.S. Woodward, “Exploring Nonlinear Couplings in Radiation Diffusion Problems,” Proceedings of the NECDC 2004.
  7. Jones, J. E., P. S. Vassilevski, and C. S. Woodward, "Nonlinear Schwarz-FAS Methods for Unstructured Finite Element Problems," proc. of Second M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, June 17-20, 2003.  Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings, pp. 2008-2011, 2003.
  8. Woodward, Carol S., Keith E. Grant, and Reed Maxwell, “Applications of Sensitivity Analysis to Uncertainty Quantification for Variably Saturated Flow,” in Computational Methods in Water Resources, S.M.Hassanizadeh, R.J. Schotting, W.G. Gray, and G.F. Pinder, eds., vol 1, Elservier, Amsterdam, (2002), 73-80.
  9. Brown, P.N., F. Graziani, I. Otero, and C.S. Woodward, “Implicit Solution of Large-Scale Radiation Diffusion Problems,” Proc. Of the Nuclear Explosives Code Developers’ Collaborations 2000, Oakland, CA, Oct. 2000. 
  10. Brown, P.N., Chang, B.; Hanebutte, U.R., Woodward, C. S., “The quest for a high performance Boltzmann transport solver,” in Applications of High-Performance Computing in Engineering VI. Sixth International Conference, Ingber, M.; Power, H.; Brebbia, C.A., eds., 2000, pp. 91-101.  
  11. Jones, J.E., and C.S. Woodward, “Preconditioning Newton–Krylov Methods for Variably Saturated Flow,” in Computational Methods in Water Resources, volume 1, L. R. Bentley, J. F. Sykes, C. A. Brebbia, W. G. Gray, and G. F. Pinder, Eds., (Rotterdam, 2000), pp 101-106.
  12. Brown, P.N.; Chang, B.; Dorr, M.R., Hannebutte, U. R., and Woodward, C. S., “Performing three-dimensional neutral particle transport calculations on tera scale computers,” in Proceedings of the High Performance Computing Symposium - HPC'99. 1999 Advanced Simulation Technologies Conference, Tentner, A. ed., 1999, pp. 76-81.
  13. Brown, P.N., B. Chang, and F. Graziani and C.S. Woodward, “Implicit Solution of Large-Scale Radiation–Material Energy Transfer Problems,” in Proceedings of the Fourth IMACS International Symposium on Iterative Methods in Scientific Computation, Iterative Methods in Scientific Computation II, International Association for Mathematics and Computers in Simulations, 1999.
  14. Hornung, Richard D., and Carol S. Woodward, “An Object-Oriented Approach for Development and Testing of Parallel Solution Algorithms for Nonlinear PDEs,” Proc. of the SIAM Workshop on Object-Oriented Methods for Inter-Operable Scientific and Engineering Computing  (SIAM, Philadelphia, PA), pp.90–98. Held in Yorktown Heights, NY, October 21–23, 1998. 
  15. Woodward, C.S., “A Newton-Krylov-Multigrid Solver for Variably Saturated Flow Problems,” Proceedings of the Twelfth International Conference on Computational Methods in Water Resources, vol. 2, pp. 609-616, Computational Mechanics Publications, Southampton, 1998.

For a long version of Dr. Woodward's CV see here.