Publications
Implicit-explicit multirate infinitesimal stage-restart methods
2023
Alex C. Fish, Daniel R. Reynolds, and Steven B. Roberts "Implicit-explicit multirate infinitesimal stage-restart methods," (submitted), 2023.
Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks
2022
John Loffeld, Andrew Nonaka, Daniel R. Reynolds, 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," (submitted), 2022.
ARKODE: a flexible IVP solver infrastructure for one-step methods
2022
Daniel R. Reynolds, David J. Gardner, Carol S. Woodward and Rujeko Chinomona "ARKODE: a flexible IVP solver infrastructure for one-step methods," (submitted), 2022.
Adaptive time step control for infinitesimal multirate methods
2022
Alex C. Fish and Daniel R. Reynolds, "Adaptive time step control for infinitesimal multirate methods," SIAM J. Sci. Comput., (accepted), 2022.
Multirate Exponential Rosenbrock Methods
2022
Vu Thai Luan, Rujeko Chinomona and Daniel R. Reynolds, "Multirate exponential Rosenbrock methods," SIAM J. Sci. Comput., 44(5), A3265-A3289, 2022.
Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers
2022
D.J. Gardner, D.R. Reynolds, C.J. Balos and C.S. Woodward, “Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers,” ACM Transactions on Mathematical Software, 48(3), 1-24, 2022.
Enabling GPU accelerated computing in the SUNDIALS time integration library
2021
C.J. Balos, D.J. Gardner, C.S. Woodward, and D.R. Reynolds “Enabling GPU accelerated computing in the SUNDIALS time integration library,” Parallel Computing, 108, 102836, 2021.
Implicit-Explicit Multirate Infinitesimal GARK Methods
2021
Rujeko Chinomona and Daniel R. Reynolds, "Implicit-Explicit Multirate Infinitesimal GARK Methods," SIAM J. Sci. Comput., 43(5), A3082-A3113, 2021.
Cyclically Parallelized Treecode for Fast Computations of Electrostatic Interactions on Molecular Surfaces
2021
Jiahui Chen, Weihua Geng and Daniel R. Reynolds, "Cyclically Parallelized Treecode for Fast Computations of Electrostatic Interactions on Molecular Surfaces," Computer Physics Communications, 260, 107742, 2021.
A New Class of High-Order Methods for Multirate Differential Equations
2020
Vu Thai Luan, Rujeko Chinomona and Daniel R. Reynolds, "A New Class of High-Order Methods for Multirate Differential Equations," SIAM J. Sci. Comput., 42(2), A1245–A1268, 2020.
ENZO: An Adaptive Mesh Refinement Code for
Astrophysics (Version 2.6)
2019
Corey Brummel-Smith, Greg Bryan, Iryna Butsky, Lauren Corlies, Andrew Emerick, John Forbes, Yusuke Fujimoto, Nathan J. Goldbaum, Philipp Grete, Cameron B. Hummels, Ji-hoon Kim, Daegene Koh, Miao Li, Yuan Li, Xinyu Li, Brian O’Shea, Molly S. Peeples, John A. Regan, Munier Salem, Wolfram Schmidt, Christine M. Simpson, Britton D. Smith, Jason Tumlinson, Matthew J. Turk, John H. Wise, Tom Abel, James Bordner, Renyue Cen, David C. Collins, Brian Crosby, Philipp Edelmann, Oliver Hahn, Robert Harkness, Elizabeth Harper-Clark, Shuo Kong, Alexei G. Kritsuk, Michael Kuhlen, James Larrue, Eve Lee, Greg Meece, Michael L. Norman, Jeffrey S. Oishi, Pascal Paschos, Carolyn Peruta, Alex Razoumov, Daniel R. Reynolds, Devin Silvia, Samuel W. Skillman, Stephen Skory, Geoffrey C. So, Elizabeth Tasker, Rick Wagner, Peng Wang, Hao Xu, and Fen Zhao, "ENZO: An Adaptive Mesh Refinement Code for Astrophysics (Version 2.6)," Journal of Open Source Software, 2019.
SUNDIALS Multiphysics+MPIManyVector Performance Testing
2019
Daniel R. Reynolds, David J. Gardner, Cody J. Balos and Carol S. Woodward, "SUNDIALS Multiphysics+MPIManyVector Performance Testing," LLNL Technical Report LLNL-TR-791538, 2019.
Evaluation of Implicit-Explicit Additive Runge-Kutta Integrators for the HOMME-NH Dynamical Core
2019
Christopher J. Vogl, Andrew Steyer, Daniel R. Reynolds, Paul A. Ullrich and Carol S. Woodward, "Evaluation of Implicit-Explicit Additive Runge-Kutta Integrators for the HOMME-NH Dynamical Core," Journal of Advances in Modeling Earth Systems, 11, 2019.
Relaxed Multirate Infinitesimal Step Methods
2019
Jean M. Sexton and Daniel R. Reynolds, "Relaxed Multirate Infinitesimal Step Methods," arXiv, 1808.03718, 2019.
Further development of efficient and accurate time integration schemes for meteorological models
2019
Vu Thai Luan, Janusz A. Pudykiewicz and Daniel R. Reynolds, "Further development of efficient and accurate time integration schemes for meteorological models," J. Computational Physics, 376:817-837, 2019.
Impacts and importance of diffusion on the spectral element method: A linear analysis
2018
Paul A. Ullrich, Daniel R. Reynolds, Jorge E. Guerra and Mark A. Taylor, "Impacts and importance of diffusion on the spectral element method: A linear analysis," J. Computational Physics, 375:427-446, 2018.
Implicit-Explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models
2018
David J. Gardner, Jorge E. Guerra, Francois P. Hamon, Daniel R. Reynolds, Paul A. Ullrich and Carol S. Woodward, "Implicit-Explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models," Geoscientific Model Development, 11:1497-1515, 2018.
Filters for improvement of multiscale data from atomistic simulations
2017
David J. Gardner and Daniel R. Reynolds, "Filters for improvement of multiscale data from atomistic simulations," SIAM J. Multiscale Model. Simul., 15:1-28, 2017.
Implicit integration methods for dislocation dynamics
2015
David J. Gardner, Carol S. Woodward, Daniel R. Reynolds, Gregg Hommes, Sylvie Aubry and A. Tom Arsenlis, "Implicit integration methods for dislocation dynamics," Modelling and Simulation in Materials Science and Engineering, 23:025006, 2015.
Fully-coupled simulation of cosmic reionization I: numerical methods and tests
2015
Michael L. Norman, Daniel R. Reynolds, Geoffrey C. So, Robert P. Harkness and John H. Wise, "Fully-coupled simulation of cosmic reionization I: numerical methods and tests," The Astrophysical Journal Supplement, 216:16, 2015.
Fully-coupled simulation of cosmic reionization II: recombinations, clumping factors, and the photon budget for reionization
2014
Geoffrey C. So, Michael L. Norman, Daniel R. Reynolds, and John H. Wise, "Fully-coupled simulation of cosmic reionization II: recombinations, clumping factors, and the photon budget for reionization," The Astrophysical Journal, 789:149, 2014.
Enzo: an adaptive mesh refinement code for astrophysics
2014
Greg L. Bryan, Michael L. Norman, Brian W. O'Shea, Tom Abel, John H. Wise, Matthew J. Turk, Daniel R. Reynolds, David C. Collins, Peng Wang, Samuel W. Skillman, Britton Smith, Robert P. Harkness, James Bordner, Ji-Hoon Kim, Michael Kuhlen, Hao Xu, Nathan Goldbaum, Cameron Hummels, Alexei G. Kritsuk, Elizabeth Tasker, Stephen Skory, Christine M. Simpson, Oliver Hahn, Jeffrey S. Oishi, Geoffrey C. So, Fen Zhao, Renyue Cen and Yuan Li, "Enzo: an adaptive mesh refinement code for astrophysics," The Astrophysical Journal Supplement, 211:19, 2014.
Multiphysics simulations: challenges and opportunities
2013
David E. Keyes et al., "Multiphysics simulations: challenges and opportunities," International Journal of High Performance Computing Applications, 27:4-83, 2013.
A fully implicit Newton-Krylov-Schwarz method for tokamak MHD: Jacobian construction and preconditioner formulation
2012
Daniel R. Reynolds, Ravi Samtaney, and Hilari C. Tiedeman, "A fully implicit Newton-Krylov-Schwarz method for tokamak MHD: Jacobian construction and preconditioner formulation," Computational Science & Discovery, 5:014003, 2012.
Sparse Jacobian construction for mapped grid visco-resistive magnetohydrodynamics
2012
Daniel R. Reynolds and Ravi Samtaney, "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, 2012.
Operator-based preconditioning of stiff hyperbolic systems
2010
Daniel R. Reynolds, Ravi Samtaney and Carol S. Woodward, "Operator-based preconditioning of stiff hyperbolic systems," SIAM Journal on Scientific Computing, 32:150-170, 2010.
Cosmological radiation hydrodynamics with Enzo
2009
Michael L. Norman, Daniel R. Reynolds and Geoffrey C. So, "Cosmological radiation hydrodynamics with Enzo," Recent Directions in Astrophysical Quantitative Spectroscopy and Radiation Hydrodynamics, AIP, 2009.
Cosmological radiative transfer codes comparison project II: the radiation-hydrodynamic tests
2009
Ilian T. Iliev, Daniel Whalen, Kyungjin Ahn, Sunghye Baek, Nickolay Y. Gnedin, Andrey V. Kravtsov, Garrelt Mellema, Michael Norman, Milan Raicevic, Daniel R. Reynolds, Daisuke Sato, Paul R. Shapiro, Benoit Semelin, Joseph Smidt, Hajime Susa, Tom Theuns and Masayuki Umemura, "Cosmological radiative transfer codes comparison project II: the radiation-hydrodynamic tests," MNRAS, 400:1283-1316, 2009.
Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization
2009
Daniel R. Reynolds, John C. Hayes, Pascal Paschos and Michael L. Norman, "Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization," Journal of Computational Physics, 228:6833-6854, 2009.
Vibration damping and heat transfer using material phase changes
2009
Petr Kloucek and Daniel R. Reynolds, "Vibration damping and heat transfer using material phase changes," U.S. Patent Number 7,506,735, issued March 24, 2009.
A Newton-Krylov solver for implicit solution of hydrodynamics in core collapse supernovae
2008
Daniel R. Reynolds, F. Douglas Swesty and Carol S. Woodward, "A Newton-Krylov solver for implicit solution of hydrodynamics in core collapse supernovae," Journal of Physics: Conference Series, 125, 2008.
Panel Discusses Research Directions and Enabling Technologies for the Future
2007
Daniel R. Reynolds and Ryan Szypowski, "Panel Discusses Research Directions and Enabling Technologies for the Future," SIAM News, May 2007.
Simulating cosmological evolution with enzo
2007
Michael L. Norman, Greg L. Bryan, Robert Harkness, James Bordner, Daniel Reynolds, Brian O'Shea and Rick Wagner, "Simulating cosmological evolution with enzo," Petascale Computing: Algorithms and Applications, D. Bader (editor), CRC Press, 2007.
Implicit solvers for large-scale nonlinear problems
2006
David E. Keyes, Daniel R. Reynolds and Carol S. Woodward, "Implicit solvers for large-scale nonlinear problems," Journal of Physics: Conference Series, 46:433-442, 2006.
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
2006
Daniel R. Reynolds, Ravi Samtaney and Carol S. Woodward, "A fully implicit numerical method for single-fluid resistive magnetohydrodynamics," Journal of Computational Physics, 219:144-162, 2006.
On the modeling of nonlinear thermodynamics in SMA wires
2006
Petr Kloucek and Daniel R. Reynolds, "On the modeling of nonlinear thermodynamics in SMA wires," Computer Methods in Applied Mechanics and Engineering, 196:180-191, 2006.
Computational modeling of vibration damping in SMA wires
2004
Petr Kloucek, Daniel R. Reynolds and Thomas I. Seidman, "Computational modeling of vibration damping in SMA wires," Continuum Mechanics and Thermodynamics, 16:495-514, 2004.
On the asymptotically stochastic computational modeling of microstructures
2004
Dennis Cox, Petr Kloucek and Daniel R. Reynolds, "On the asymptotically stochastic computational modeling of microstructures," Future Generation Computer Systems, 20: 409-424, 2004.
Stochastic relaxation of variational integrals with non-attainable infima
2004
Dennis D. Cox, Petr Kloucek, Daniel R. Reynolds and Pavel Solin, "Stochastic relaxation of variational integrals with non-attainable infima," in Proc.: ENUMATH 2003 European Conference on Numerical Mathematics, Springer-Verlag, Berlin, 239-249, 2004.
A nonlinear thermodynamic model for phase transitions in shape memory alloy wires
2003
Daniel R. Reynolds, "A nonlinear thermodynamic model for phase transitions in shape memory alloy wires," Ph.D. Thesis, Rice University Department of Computational and Applied Mathematics, May 2003.
Thermal stabilization of shape memory alloy wires
2003
Petr Kloucek, Daniel R. Reynolds and Thomas I. Seidman, "Thermal stabilization of shape memory alloy wires," in Smart Structures and Materials 2003: Modeling, Signal Processing, and Control, R.C. Smith editor, Proc. of SPIE, vol. 5049, 2003.
On thermodynamic active control of shape memory alloy wires
2003
Petr Kloucek, Daniel R. Reynolds and Thomas I. Seidman, "On thermodynamic active control of shape memory alloy wires," Systems and Control Letters, 48(3-4): 211-219, 2003.
The computational modeling of crystalline materials using a stochastic variational principle
2002
Dennis Cox, Petr Kloucek and Daniel R. Reynolds, "The computational modeling of crystalline materials using a stochastic variational principle," in Lecture Notes in Computer Science 2330: 461-469, 2002.
A subgrid projection method for relaxation of non-attainable differential inclusions
2002
Dennis Cox, Petr Kloucek and Daniel R. Reynolds, "A subgrid projection method for relaxation of non-attainable differential inclusions," in Proc.: ENUMATH 2001 European Conference on Numerical Mathematics, Springer-Verlag, Berlin, 2002.
Efficient and automatic implementation of the adjoint state method
2002
Mark S. Gockenbach, Daniel R. Reynolds, Peng Shen, and William W. Symes, "Efficient and automatic implementation of the adjoint state method," ACM Transactions on Mathematical Software, 28(1): 22-44, 2002.
Second order solution of Fritz John's ultrahyperbolic PDE for volumetric computed tomography
2001
Jicun Hu, Chris Ingrassia, Svenja Lowitzsch, Jang Park, Angel Pineda, Daniel Reynolds, Nicholas Valdivia (S.K. Patch, mentor), "Second order solution of Fritz John's ultrahyperbolic PDE for volumetric computed tomography," IMA preprint 1752-4, 2001.
Automatic differentiation and the adjoint state method
2001
Mark S. Gockenbach, Daniel R. Reynolds, and William W. Symes, "Automatic differentiation and the adjoint state method," in Automatic Differentiation of Algorithms: From Simulation to Optimization, Springer-Verlag, 161-165, 2001.