
Title
Distinguished Member of the Technical Staff 
Email
woodward6@llnl.gov 
Phone
(925) 4246013 
Organization
Not Available
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 nonequilibrium 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 midcareer scientists and engineers recognized by LLNL for exceptional technical achievement. She served as the Society for Industrial and Applied Mathematics (SIAM) Vice PresidentatLarge (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 AtLarge 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 https://en.wikipedia.org/wiki/Carol_S._Woodward
For ORC ID information, see: orcid.org/0000000265028659
Refereed Journal and Conference Papers
 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. https://doi.org/10.1145/3539801.
 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. 4959. https://epubs.siam.org/doi/abs/10.1137/1.9781611977141.5.
 Balos CJ, Gardner DJ, Woodward CS, Reynolds DR. “Enabling GPU Accelerated Computing in the SUNDIALS Time Integration Library,” Parallel Computing, 108, Dec. 2021. https://doi.org/10.1016/j.parco.2021.102836.
 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 LargeScale Systems (ScalA), 2021, pp. 3543, https://doi.org/10.1109/ScalA54577.2021.00010.
 Roberts S, Loffeld J, Sarshar A, Woodward CS, Sandu A., “Implicit multirate GARK methods,” Journal of Scientific Computing 87.1 (2021): 132. https://doi.org/10.1007/s1091502001400z.
 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.
 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.
 S. Guenther, R. D. Falgout, P. Top, C. S. Woodward, and J. Schroder, “ParallelinTime Solution of Power Systems with Unscheduled Events,” proceedings of the 2020 IEEE Power and Energy Society General Meeting (PESGM).
 B. Kuffuor, N. Engdahl, C. Woodward, L. Condon, S. Kollet, and R. Maxwell, “Simulating Coupled SurfaceSubsurface Flows with ParFlow v3.5.0: Capabilities, applications, and ongoing development of an opensource, massively parallel, integrated hydrologic model,” Geoscientific Model Development, 13(3), 13731397, 10.5194/gmd1313732020, 2020.
 M. Lecouvez, R. D. Falgout, and C. S. Woodward, “A parallelintime algorithm for variable step multistep methods,” Journal of Computational Science, 37, p.101029, 2019.
 Vogl, Christopher J., Andrew Steyer, Daniel R. Reynolds, Paul A. Ullrich, and Carol S. Woodward. "Evaluation of ImplicitExplicit Additive RungeKudda Integrators for the HOMMENH Dynamical Core." Journal of Advances in Modeling Earth Systems, 11(12), p.42284244, https://doi.org/10.1029/2019MS00170, 2019.
 S. Zhang, H. Wan, P. Rasch, B. Singh, V. Larsen, and C. Woodward, “An objective and efficient method for assessing the impact of reducedprecision calculations on solution correctness,” Journal of Advances in Modeling Earth Systems, 11, 31313147. https://doi.org/10.1029/2019MS001817, 2019.
 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 LargeScale Heterogeneous System,” In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, p. 32. ACM, 2019.
 J. B. Schroder, M. Lecouvez, R. D. Falgout, C. S. Woodward, and P. Top, "ParallelinTime Solution of Power Systems with Scheduled Events," IEEE Power and Energy Society General Meeting (PESGM), pp. 1–5, IEEE, 2018.
 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 nonhydrostatic atmospheric models," Geosci. Model Dev., 11, 14971515, https://doi.org/10.5194/gmd1114972018, 2018.
 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 fullyimplicit solvers within a spectralelement shallowwater atmosphere model,” International Journal of High Performance Computing Applications, DOI: 10.1177/109434201773637
 J. Loffeld and C. S. Woodward, "Considerations on the implementation and use of Anderson acceleration on distributed memory and GPUbased 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.
 W. Collins, K. J. Evans, H. Johansen, C. S. Woodward, and P. Caldwell, “Progress in Fast, Accurate Multiscale Climate Simulations,” Procedia Computer Science, 51, (2015), pp. 20062015. DOI: 10.1016/j.procs.2015.05.465.
 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. 15. IEEE, 2016.
 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. 137176. Springer New York, 2016.
 C. S. Woodward, D. J. Gardner, and K. J. Evans, “On the Use of Finite Difference MatrixVector Products in NewtonKrylov Solvers for Implicit Climate Dynamics with Spectral Elements,” Procedia Computer Science, 51, (2015), pp. 20362045. DOI: 10.1016/j.procs.2015.05.468.
 P. A. Lott, C. S. Woodward, and K. J. Evans, “Algorithmically Scalable Block Preconditioner for Fully Implicit ShallowWater Equations in CAMSE,” Computational Geosciences, 19(1), 2015, pp. 4961. DOI: 10.1007/s1059601494476.
 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 Cosimulation,” in refereed proceedings of 2015 Workshop on Modeling and Simulation of CyberPhysical Energy Systems (MSCPES), Seattle, WA, April 2015.
 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.
 D. OseiKuffuor, 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.
 S. Smith, C. Woodward, L. Min, C. Jing, A. Del Rosso, “OnLine 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.
 J. M. Connors, J. W. Banks, J. A. F. Hittinger, C. S. Woodward, “Quantification of Errors for OperatorSplit AdvectionDiffusion Calculations,” Computer Methods in Applied Mechanics and Engineering, Vol. 272, pp. 181197, Apr., 2014. DOI: 10.1016/j.cma.2014.01.005.
 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. 894926. DOI: 10.1137/110845100.
 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. 3542. DOI: 10.1090/conm/586/11646.
 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.
 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. 92101. DOI: 10.1016/j.advwatres.2011.12.013.
 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. 115, 2012. DOI: 10.1016/j.cma.2011.11.021.
 Reed M. Maxwell, Julie K. Lundquist, Jeff Mirocha, Steven G. Smith, Carol S. Woodward, and Andrew F.B. Tompson, “Development of a coupled groundwateratmospheric model,” Monthly Weather Review, 139(1), 2011, pp. 96–116. DOI: 10.1175/2010MWR3392.1.
 Kollet S., Maxwell R., Woodward C.S., et al., “Proofofconcept of regional scale hydrologic simulations at hydrologic resolution utilizing massively parallel computer resources,” Water Resour. Res., 46, 2010, W04201, doi:10.1029/2009WR008730, 17. Featured Article with Water Resources Research (given to only 5% of accepted papers).
 Reynolds, D.R., R. Samtaney, and C.S. Woodward, “OperatorBased Preconditioning of Stiff Hyperbolic Systems,” SIAM J. on Sci. Comp., 32(1), pp. 150170, 2010. DOI: 10.1137/080713331.
 Reynolds, D.R., Swesty, D.O., and Woodward, C.S., “A NewtonKrylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae,” 2008 J. Phys.: Conf. Ser. 125 012085. DOI: 10.1088/17426596/125/1/012085.
 Brown, P. N., H. F. Walker, R. Wasyk, and C. S. Woodward, “On using approximate finitedifferences in matrixfree NewtonKrylov methods,” SIAM J. Numer. Anal., 46 (2007), pp. 1892–1911. DOI: 10.1137/060652749.
 D. R. Reynolds, R. Samtaney and C. S. Woodward, “A fully implicit numerical method for singlefluid resistive magnetohydrodynamics,” Journal of Computational Physics, 219(1), (2006), pp 144162. DOI: 10.1016/j.jcp.2006.03.022.
 D. E. Keyes, D. R. Reynolds and C. S. Woodward, "Implicit solvers for largescale nonlinear problems," Journal of Physics:
Conference Series, 46:433442, 2006. DOI: 10.1088/17426596/46/1/060.  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.
 Brown Peter N., Dana E. Shumaker, and Carol S. Woodward, “Fully Implicit Solution of LargeScale NonEquilibrium Radiation Diffusion with High Order Time Integration,” J. Comp. Phys., 204(2), (2005), pp. 760783. DOI: 10.1016/j.jcp.2004.10.031.
 Lee, S. L., C. S. Woodward, and F. R. Graziani, “Analyzing Radiation Diffusion Using TimeDependent SensitivityBased Techniques,” Journal of Computational Physics, 192, (1), (2003), pp. 211230. DOI: 10.1016/j.jcp.2003.07.031.
 Brown, P. N., P. Vassilevski, and C. S. Woodward, “On MeshIndependent Convergence of an Inexact NewtonMultigrid Algorithm,” SIAM J. Sci. Comput., 25, (2), (2003), pp. 570590. DOI: 10.1137/S1064827502407822.
 Brown, P.N., and C.S. Woodward, “Preconditioning Strategies for Fully Implicit Radiation Diffusion with MaterialEnergy Transfer,” SIAM J. Sci. Comput., 23, (2), (2001), pp. 499516. DOI: 10.1137/S106482750037295X.
 Jones, J.E., and C.S. Woodward, “NewtonKrylovMultigrid Solvers for LargeScale, Highly Heterogeneous, Variably Saturated Flow Problems,” Adv. Water Resources, 24, (July 2001), pp. 763774. DOI: 10.1016/S03091708(00)000750.
 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), 701724. DOI: 10.1137/S0036142996311040.
 Dawson, C.N., M.F. Wheeler, and C.S. Woodward, “A TwoGrid Finite Difference Scheme for Nonlinear Parabolic Equations,” SIAM J. Numerical Analysis, 35, (2/1998). DOI: 10.1137/S0036142995293493.
 Dawson, C.N., H. Klie, M.F. Wheeler, and C.S. Woodward, “A Parallel, Implicit, CellCentered Method for TwoPhase Flow with a Preconditioned Newton–Krylov Solver,” Computational Geosciences, 1, (3/4,1997), 215–249.
 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
 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 1014, 2011, http://press.mcs.anl.gov/scidac2011/.
 C.S. Woodward and J.A.F. Hittinger, “Numerical Convergence Studies of Weapon Calculations,” Proceedings of the 2010 NECDC, Los Alamos, NM, Oct. 2010.
 Walker, H.F., C.S. Woodward, and U.M. Yang, “An Accelerated FixedPoint 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. 216223, 2010.
 Anderson, S., B. Bihari, K. Salari, and C. S. Woodward, “Code Verification Results of an LLNL ASC Code on Some TriLab Verification Test Suite Problems,” proceedings of the NECDC 2006.
 Shumaker, Dana E. and Carol S. Woodward, “Implicit Solution of NonEquilibrium Radiation Diffusion Including Reactive Heating Source in Material Energy Equation,” in “Computational Methods in Transport,” F. Graziani, ed., Springer, Berlin, (2006), pp. 353370.
 Miller, D.S. and C.S. Woodward, “Exploring Nonlinear Couplings in Radiation Diffusion Problems,” Proceedings of the NECDC 2004.
 Jones, J. E., P. S. Vassilevski, and C. S. Woodward, "Nonlinear SchwarzFAS Methods for Unstructured Finite Element Problems," proc. of Second M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, June 1720, 2003. Computational Fluid and Solid Mechanics 2003, Vols 1 and 2, Proceedings, pp. 20082011, 2003.
 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), 7380.
 Brown, P.N., F. Graziani, I. Otero, and C.S. Woodward, “Implicit Solution of LargeScale Radiation Diffusion Problems,” Proc. Of the Nuclear Explosives Code Developers’ Collaborations 2000, Oakland, CA, Oct. 2000.
 Brown, P.N., Chang, B.; Hanebutte, U.R., Woodward, C. S., “The quest for a high performance Boltzmann transport solver,” in Applications of HighPerformance Computing in Engineering VI. Sixth International Conference, Ingber, M.; Power, H.; Brebbia, C.A., eds., 2000, pp. 91101.
 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 101106.
 Brown, P.N.; Chang, B.; Dorr, M.R., Hannebutte, U. R., and Woodward, C. S., “Performing threedimensional 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. 7681.
 Brown, P.N., B. Chang, and F. Graziani and C.S. Woodward, “Implicit Solution of LargeScale 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.
 Hornung, Richard D., and Carol S. Woodward, “An ObjectOriented Approach for Development and Testing of Parallel Solution Algorithms for Nonlinear PDEs,” Proc. of the SIAM Workshop on ObjectOriented Methods for InterOperable Scientific and Engineering Computing (SIAM, Philadelphia, PA), pp.90–98. Held in Yorktown Heights, NY, October 21–23, 1998.
 Woodward, C.S., “A NewtonKrylovMultigrid Solver for Variably Saturated Flow Problems,” Proceedings of the Twelfth International Conference on Computational Methods in Water Resources, vol. 2, pp. 609616, Computational Mechanics Publications, Southampton, 1998.