Efficient and Flexible Multirate Temporal Adaptivity
Published in arXiv, 2025
Recommended citation: Reynolds, D.R., Amihere, S., Mitchell, D., Luan, V.T. (2025). "Efficient and Flexible Multirate Temporal Adaptivity" arXiv:2510.14964.
Download Paper
Published in arXiv, 2025
Recommended citation: Reynolds, D.R., Amihere, S., Mitchell, D., Luan, V.T. (2025). "Efficient and Flexible Multirate Temporal Adaptivity" arXiv:2510.14964.
Download Paper
Published in arXiv, 2025
Recommended citation: Roberts, S.B., Aggul, M., Reynolds, D.R., Balos, C.J., Gardner, D.J., Woodward, C.S. (2025). "New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0" arXiv:2506.14976.
Download Paper
Published in International Journal of High Performance Computing Applications, 2024
Recommended citation: Balos, C.J., Day, M., Esclapez, L., Felden, A.M., Gardner, D.J., Hassanaly, M., Reynolds, D.R., Rood, J., Sexton, J.M., Wimer, N.T., Woodward, C.S. (2024). "SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems; International Journal of High Performance Computing Applications.
Download Paper
Published in Computer Physics Communications, 2024
Recommended citation: Yang, X., Sliheet, E., Iriye, R., Reynolds, D.R., and Geng, W. (2024). "Optimized parallelization of boundary integral Poisson-Boltzmann solvers." Computer Physics Communications, 299:109125.'
Download Paper
Published in Journal of Computational and Applied Mathematics, 2024
Recommended citation: Fish, A.C., Reynolds, D.R., and Roberts, S.B. (2024). "Implicit-explicit multirate infinitesimal stage-restart methods." Journal of Computational and Applied Mathematics, 438:115534.
Download Paper
Published in International Journal of High Performance Computing Applications, 2024
Recommended citation: Loffeld, J., Nonaka, A., Reynolds, D.R., Gardner, D.J., and Woodward, C.S. (2024). "Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks." International Journal of High Performance Computing Applications.
Download Paper
Published in Astrochemical Modeling: Practical Aspects of Microphysics in Numerical Simulations, 2023
Recommended citation: Reynolds, D.R. (2023). "Time-dependent integration of chemical networks." in Astrochemical Modeling: Practical Aspects of Microphysics in Numerical Simulations. S. Bovino and T. Grasso (ed.), Elsevier.
Download Paper
Published in ACM Transactions on Mathematical Software, 2023
Recommended citation: Reynolds, D.R., Gardner, D.J., Woodward, C.S., and Chinomona, R. (2023). "ARKODE: a flexible IVP solver infrastructure for one-step methods." ACM Transactions on Mathematical Software, 49(2):1-26.
Download Paper
Published in SIAM Journal on Scientific Computing, 2023
Recommended citation: Fish, A.C. and Reynolds, D.R. (2023). "Adaptive time step control for infinitesimal multirate methods." SIAM Journal on Scientific Computing, 45(2):A958-A984.
Download Paper
Published in SIAM Journal on Scientific Computing, 2022
Recommended citation: Luan, V.T., Chinomona, R., and Reynolds, D.R. (2022). "Multirate exponential Rosenbrock methods." SIAM Journal on Scientific Computing, 44(5):A3265-A3289.
Download Paper
Published in ACM Transactions on Mathematical Software, 2022
Recommended citation: Gardner, D.J., Reynolds, D.R., Balos, C.J. and Woodward, C.S. (2022). "Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers." ACM Transactions on Mathematical Software, 48(3):1-24.
Download Paper
Published in Parallel Computing, 2021
Recommended citation: Balos, C.J., Gardner, D.J., Woodward, C.S., and Reynolds, D.R.. (2021). "Enabling GPU accelerated computing in the SUNDIALS time integration library." Parallel Computing, 108:102836.
Download Paper
Published in SIAM Journal on Scientific Computing, 2021
Recommended citation: Chinomona, R. and Reynolds, D.R.. (2021). "Implicit-explicit multirate infinitesimal GARK methods." SIAM Journal on Scientific Computing, 43(5):A3082-A3113.
Download Paper
Published in Computer Physics Communications, 2021
Recommended citation: Chen, J., Geng, W., and Reynolds, D.R. (2021). "Cyclically parallelized treecode for fast computations of electrostatic interactions on molecular surfaces." Computer Physics Communications, 260:107742.
Download Paper
Published in SIAM Journal on Scientific Computing, 2020
Recommended citation: Luan, V.T., Chinomona, R., and Reynolds, D.R. (2020). "A new class of high-order methods for multirate differential equations." SIAM Journal on Scientific Computing, 42(2):A1245-A1268.
Download Paper
Published in Journal of Open Source Software, 2019
Recommended citation: Brummel-Smith, C., Bryan, G., Butsky, I., Corlies, L., Emerick, A., Forbes, J., Fujimoto, Y., Goldbaum, N.J., Grete, P., Hummels, C.B., Kim, J.-H., Koh, D., Li, M., Li, Y., Li, X., O'Shea, B., Peeples, M.S., Regan, J.A., Salem, M., Schmidt, W., Simpson, C.M., Smith, B.D., Tumlinson, J., Turk, M.J., Wise, J.H., Abel, T., Bordner, J., Cen, R., Collins, D.C., Crosby, B., Edelmann, P., Hahn, O., Harkness, R., Harper-Clark, E., Kong, S., Kritsuk, A.G., Kuhlen, M., Larrue, J., Lee, E., Meece, G., Norman, M.L., Oishi, J.S., Paschos, P., Peruta, C., Razoumov, A., Reynolds, D.R., Silvia, D., Skillman, S.W., Skory, S., So, G.C., Tasker, E., Wagner, R., Wang, P., Xu, H., and Zhao, F. (2019). "ENZO: An Adaptive Mesh Refinement Code for Astrophysics (Version 2.6)." Journal of Open Source Software, 4(42):1638.
Download Paper
Published in LLNL Technical Report, 2019
Recommended citation: Reynolds, D.R., Gardner, D.J., Balos, C.J., and Woodward, C.S.. (2019). "SUNDIALS multiphysics+MPIManyVector performance testing." LLNL Technical Report, LLNL-TR-791538.
Download Paper
Published in Journal of Advances in Modeling Earth Systems, 2019
Recommended citation: Vogl, C.J., Steyer, A., Reynolds, D.R., Ullrich, P.A., and Woodward, C.S. (2019). "Evaluation of implicit-explicit additive Runge-Kutta integrators for the HOMME-NH dynamical core." Journal of Advances in Modeling Earth Systems, 11(12):4228-4244.
Download Paper
Published in arXiv, 2019
Recommended citation: Sexton, J.M. and Reynolds, D.R. (2019). "Relaxed multirate infinitesimal step methods." arXiv, 1808.03718.
Download Paper
Published in Journal of Computational Physics, 2019
Recommended citation: Luan, V.T., Pudykiewicz, J.A., and Reynolds, D.R. (2019). "Further development of efficient and accurate time integration schemes for meteorological models." Journal of Computational Physics, 376:817-837.
Download Paper
Published in Journal of Computational Physics, 2018
Recommended citation: Ullrich, P.A., Reynolds, D.R., Guerra, J.E., and Taylor, M.A. (2018). "Impacts and importance of diffusion on the spectral element method: a linear analysis." Journal of Computational Physics, 375:427-446.
Download Paper
Published in Geoscientific Model Development, 2018
Recommended citation: Gardner, D.J., Guerra, J.E., Hamon, F.P., Reynolds, D.R., Ullrich, P.A., and Woodward, C.S. (2018). "Implicit-explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models." Geoscientific Model Development, 11(4):1497-1515.
Download Paper
Published in SIAM Journal on Multiscale Modeling and Simulation, 2017
Recommended citation: Gardner, D.J. and Reynolds, D.R. (2017). "Filters for improvement of multiscale data from atomistic simulations." SIAM Journal on Multiscale Modeling and Simulation, 15(1):1-28.
Download Paper
Published in Modelling and Simulation in Materials Science and Engineering, 2015
Recommended citation: Gardner, D.J., Woodward, C.S., Reynolds, D.R., Hommes, G., Aubry, S., and Arsenlis, A.T. (2015). "Implicit integration methods for dislocation dynamics." Modelling and Simulation in Materials Science and Engineering, 23:025006.
Download Paper
Published in The Astrophysical Journal Supplement, 2015
Recommended citation: Norman, M.L., Reynolds, D.R., So, G.C., Harkness, R.P., and Wise, J.H. (2015). "Fully-coupled simulation of cosmic reionization I: numerical methods and tests." The Astrophysical Journal Supplement, 216(1):16.
Download Paper
Published in The Astrophysical Journal, 2014
Recommended citation: So, G.C., Norman, M.L., Reynolds, D.R., and Wise, J.H. (2014). "Fully-coupled simulation of cosmic reionization II: recombinations, clumping factors, and the photon budget for reionization." The Astrophysical Journal, 789(2):149.
Download Paper
Published in The Astrophysical Journal Supplement, 2014
Recommended citation: Bryan, G.L., Norman, M.L., O'Shea, B.W., Abel, T., Wise, J.H., Turk, M.J., Reynolds, D.R., Collins, D.C., Wang, P., Skillman, S.W., Smith, B., Harkness, R.P., Bordner, J., Kim, J.-H., Kuhlen, M., Xu, H., Goldbaum, N., Hummels, C., Kritsuk, A.G., Tasker, E., Skory, S., Simpson, C.M., Hahn, O., Oishi, J.S., So, G.C., Zhao, F., Cen, R., and Li, Y. (2014). "Enzo: an adaptive mesh refinement code for astrophysics." The Astrophysical Journal Supplement, 211(2):19.
Download Paper
Published in International Journal of High Performance Computing Applications, 2013
Recommended citation: Keyes, D.E., McInnes, L.C., Woodward, C.S., Gropp, W., Myra, E., Pernice, M., Bell, J., Brown, J., Clo, A., Connors, J., Constantinescu, E., Estep, D., Evans, K., Farhat, C., Hakim, A., Hammond, G., Hansen, G., Hill, J., Isaac, T., Jiao, X., Jordan, K., Kaushik, D., Kaxiras, E., Koniges, A., Lee, K., Lott, A., Lu, Q., Magerlein, J., Maxwell, R., McCourt, M., Mehl, M., Pawlowski, R., Randles, A.P., Reynolds, D.R., Riviere, B., Rude, U., Scheibe, T., Shadid, J., Sheehan, B., Shephard, M., Siegel, A., Smith, B., Tang, X., Wilson, C., and Wohlmuth, B. (2013). "Multiphysics simulations: challenges and opportunities." International Journal of High Performance Computing Applications, 27(1):4-83.
Download Paper
Published in Computational Science & Discovery, 2012
Recommended citation: Reynolds, D.R., Samtaney, R., and Tiedeman, H.C. (2012). "A fully implicit Newton-Krylov-Schwarz method for tokamak MHD: Jacobian construction and preconditioner formulation." Computational Science & Discovery, 5(1):014003.
Download Paper
Published in Lecture Notes in Computational Science and Engineering, 2012
Recommended citation: Reynolds, D.R. and Samtaney, R. (2012). "Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics." in Recent Advances in Algorithmic Differentiation, Lecture Notes in Computational Science and Engineering, vol. 87, Springer.
Download Paper
Published in SIAM Journal on Scientific Computing, 2010
Recommended citation: Reynolds, D.R., Samtaney, R. and Woodward, C.S. (2010). "Operator-based preconditioning of stiff hyperbolic systems." SIAM Journal on Scientific Computing, 32(1):150-170.
Download Paper
Published in Recent Directions in Astrophysical Quantitative Spectroscopy and Radiation Hydrodynamics, 2009
Recommended citation: Norman, M.L., Reynolds, D.R., and So, G.C. (2009). "Cosmological radiation hydrodynamics with Enzo." Recent Directions in Astrophysical Quantitative Spectroscopy and Radiation Hydrodynamics, AIP.
Download Paper
Published in Monthly Notices of the Royal Astronomical Society, 2009
Recommended citation: Iliev, I.T., Whalen, D., Ahn, K., Baek, S., Gnedin, N.Y., Kravtsov, A.V., Mellema, G., Norman, M., Raicevic, M., Reynolds, D.R., Sato, D., Shapiro, P.R., Semelin, B., Smidt, J., Susa, H., Theuns, T., and Umemura, M. (2009). "Cosmological radiative transfer codes comparison project II: the radiation-hydrodynamic tests." Monthly Notices of the Royal Astronomical Society, 400(3):1283-1316.
Download Paper
Published in Journal of Computational Physics, 2009
Recommended citation: Reynolds, D.R., Hayes, J.C., Paschos, P. and Norman, M.L. (2009). "Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization." Journal of Computational Physics, 228(18):6833-6854.
Download Paper
Published in U.S. Patent Office, 2009
Recommended citation: Kloucek, P. and Reynolds, D.R. (2009). "Vibration damping and heat transfer using material phase changes." U.S. Patent Number 7.506.735.
Download Paper
Published in Journal of Physics: Conference Series, 2008
Recommended citation: Reynolds, D.R., Swesty, F.D., and Woodward, C.S. (2008). "A Newton-Krylov solver for implicit solution of hydrodynamics in core collapse supernovae." Journal of Physics: Conference Series, 125:012085.
Download Paper
Published in SIAM News, 2007
Recommended citation: Reynolds, D.R. and Szypowski, R. (2007). "Panel discusses research directions and enabling technologies for the future." SIAM News, 40(4).
Download Paper
Published in Petascale Computing: Algorithms and Applications, 2007
Recommended citation: Norman, M.L., Bryan, G.L., Harkness, R., Bordner, J., Reynolds, D.R., O'Shea, B. and Wagner, R. (2007). "Simulating cosmological evolution with Enzo." in Petascale Computing: Algorithms and Applications, D. Bader (ed.), CRC Press.
Download Paper
Published in Journal of Physics: Conference Series, 2006
Recommended citation: Keyes, D.E., Reynolds, D.R., and Woodward, C.S. (2006). "Implicit solvers for large-scale nonlinear problems." Journal of Physics: Conference Series, 46:433.
Download Paper
Published in Journal of Computational Physics, 2006
Recommended citation: Reynolds, D.R., Samtaney, R. and Woodward, C.S. (2006). "Paper Title Number 1." Journal of Computational Physics, 219(1):144-162.
Download Paper
Published in Computer Methods in Applied Mechanics and Engineering, 2006
Recommended citation: Kloucek, P. and Reynolds, D.R. (2006). "On the modeling of nonlinear thermodynamics in SMA wires." Computer Methods in Applied Mechanics and Engineering, 196(1):180-191.
Download Paper
Published in Continuum Mechanics and Thermodynamics, 2004
Recommended citation: Kloucek, P., Reynolds, D.R., and Seidman, T.I. (2004). "Computational modeling of vibration damping in SMA wires." Continuum Mechanics and Thermodynamics, 16:495-514.
Download Paper
Published in Future Generation Computer Systems, 2004
Recommended citation: Cox, D., Kloucek, P., and Reynolds, D.R.. (2004). "On the asymptotically stochastic computational modeling of microstructures." Future Generation Computer Systems, 20(3):409-424.
Download Paper
Published in Proc.: ENUMATH 2003 European Conference on Numerical Mathematics, 2004
Recommended citation: Cox, D.D., Kloucek, P., Reynolds, D.R., and Solin, P. (2004). "Stochastic relaxation of variational integrals with non-attainable infima." In: Feistauer, M., Dolejsi, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications, Springer, Berlin, Heidelberg, 239-249.
Download Paper
Published in Ph.D. Thesis, Rice University Department of Computational and Applied Mathematics, 2003
Recommended citation: Reynolds, D.R. (2003). "A nonlinear thermodynamic model for phase transitions in shape memory alloy wires." Ph.D. Thesis, Rice University Department of Computational and Applied Mathematics.
Download Paper
Published in Proc. SPIE 5049, Smart Structures and Materials 2003: Modeling, Signal Processing, and Control, 2003
Recommended citation: Kloucek, P., Reynolds, D.R., and Seidman, T.I. (2003). "Thermal stabilization of shape memory alloy wires." in Proc. SPIE 5049, Smart Structures and Materials 2003: Modeling, Signal Processing, and Control
Download Paper
Published in Systems and Control Letters, 2003
Recommended citation: Kloucek, P., Reynolds, D.R., and Seidman, T.I. (2003). "On thermodynamic active control of shape memory alloy wires." Systems and Control Letters, 48(3-4):211-219.
Download Paper
Published in Lecture Notes in Computer Science, 2002
Recommended citation: Cox, D., Kloucek, P., and Reynolds, D.R. (2002). "The computational modeling of crystalline materials using a stochastic variational principle." In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science -- ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2330. Springer, Berlin, Heidelberg.
Download Paper
Published in Numerical Mathematics and Advanced Applications, 2002
Recommended citation: Cox, D., Kloucek, P., and Reynolds, D.R. (2002). "A subgrid projection method for relaxation of non-attainable differential inclusions." In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano
Download Paper
Published in ACM Transactions on Mathematical Software, 2002
Recommended citation: Gockenbach, M.S., Reynolds, D.R., Shen, P., and Symes, W.W. (2009). "Efficient and automatic implementation of the adjoint state method." ACM Transactions on Mathematical Software. 28(1):22-44
Download Paper
Published in IMA Preprints Series, 2001
Recommended citation: Hu, J., Ingrassia, C., Lowitzsch, S., Park, J., Pineda, A., Reynolds, D.R., and Valdivia, N. (S.K. Patch, mentor). (2001). "Second order solution of Fritz John's ultrahyperbolic PDE for volumetric computed tomography." IMA Preprints Series, 1752-4.
Download Paper
Published in Automatic Differentiation of Algorithms, 2001
Recommended citation: Gockenbach, M.S., Reynolds, D.R., and Symes, W.W. (2001). "Automatic differentiation and the adjoint state method." In: Corliss, G., Faure, C., Griewank, A., Hascoet, L., Naumann, U. (eds) Automatic Differentiation of Algorithms. Springer, New York, NY.
Download Paper