(he/him/his)

Computational mathematician, focused on large-scale scientific computation.

Posts by Collection

publications

Automatic differentiation and the adjoint state method

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

The computational modeling of crystalline materials using a stochastic variational principle

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

Thermal stabilization of shape memory alloy wires

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

Stochastic relaxation of variational integrals with non-attainable infima

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

Simulating cosmological evolution with Enzo

Published in Petascale Computing: Algorithms and Applications, 2007

arXiv eprint

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

Cosmological radiative transfer codes comparison project II: the radiation-hydrodynamic tests

Published in Monthly Notices of the Royal Astronomical Society, 2009

arXiv eprint

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

Cosmological radiation hydrodynamics with Enzo

Published in Recent Directions in Astrophysical Quantitative Spectroscopy and Radiation Hydrodynamics, 2009

arXiv eprint

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

Multiphysics simulations: challenges and opportunities

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

Enzo: an adaptive mesh refinement code for astrophysics

Published in The Astrophysical Journal Supplement, 2014

arXiv eprint

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

Implicit integration methods for dislocation dynamics

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

ENZO: An Adaptive Mesh Refinement Code for Astrophysics (Version 2.6)

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

Time-dependent integration of chemical networks

Published in Astrochemical Modeling: Practical Aspects of Microphysics in Numerical Simulations, 2023

Publisher site

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

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Published in International Journal of High Performance Computing Applications, 2024

arXiv eprint

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

SUNDIALS time integrators for exascale applications with many independent ODE systems

Published in International Journal of High Performance Computing Applications, 2024

arXiv eprint

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

software

ARKODE

Adaptive Runge Kutta solvers for systems of Ordinary Differential Equations

SUNDIALS

SUite of Nonlinear Differential and ALgebraic Solvers

RKLab

Runge–Kutta exploration framework

GX

GPU-native nonlinear gyrokinetics

Gkeyll

Discontinuous Galerkin plasma physics

BOUT++

Plasma simulation in curvilinear coordinate systems

Enzo

Astrophysical adaptive mesh refinement simulation framework

Tempest

Tempest atmosphere / Earth-system model

talks

teaching

CAAM 335 – Matrix Analysis (Teaching Assistant)

Undergraduate, Rice University, Department of Computational and Applied Mathematics

Equilibria and the solution of linear systems and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration. Optional 1-credit laboratory motivates concepts from the course via physical experiments involving circuits, spring networks, and vibrating mechanical systems.

Math 20D – Introduction to Differential Equations

Undergraduate, University of California, San Diego

Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients, variations of parameters. Systems. Series solutions. Laplace transforms. Techniques for engineering sciences. Computing symbolic and graphical solutions using MATLAB.

Math 174 – Numerical Methods in Science and Engineering

Undergraduate, University of California, San Diego

Floating point arithmetic, direct and iterative solution of linear equations, iterative solution of nonlinear equations, optimization, approximation theory, interpolation, quadrature, numerical methods for initial and boundary value problems in ordinary differential equations.

SMU HPC Workshops

Graduate, Southern Methodist University, Department of Mathematics

Inaugural SMU HPC workshops, sponsored by the SMU Center for Scientific Computation. These focused on general high-performance computing computing, with specific instruction on using the new SMU ManeFrame cluster.

Math 3302 – Calculus 3 / Multivariable Calculus

Undergraduate, Southern Methodist University, Department of Mathematics

A continuation of Calculus 2. Topics include arametric equations, polar coordinates, partial differentiation, multiple integrals, and vector analysis.

Math 3304 – Introduction to Linear Algebra

Undergraduate, Southern Methodist University, Department of Mathematics

Matrices and linear equations, Gaussian elimination, determinants, rank, geometrical notions, eigenvalue problems, and coordinate transformations, norms, inner products, orthogonal projections, Gram-Schmidt and least squares.

Math 3315 – Introduction to Scientific Computing

Undergraduate, Southern Methodist University, Department of Mathematics

An elementary survey course that includes techniques for root-finding, interpolation, functional approximation, numerical differentiation and numerical integration. Special attention is given to MATLAB programming, algorithm implementations, and library codes. Students registering for this course must also register for an associated computer laboratory.

Math 3316 – Introduction to High-Performance Scientific Computing

Undergraduate, Southern Methodist University, Department of Mathematics

An elementary survey course that includes techniques for root-finding, interpolation, functional approximation, linear equations, and numerical integration. Computational work focuses on the Python and C++ programming languages using Linux.

Math 4315 – Advanced Scientific Computing

Undergraduate, Southern Methodist University, Department of Mathematics

Advanced algorithms central to scientific and engineering computing. Topics include solution of linear systems of equations, functional approximation, initial-value problems, and boundary-value problems. Special attention is given to algorithm derivation and implementation.

Math 5315 – Introduction to Numerical Analysis

Undergraduate, Southern Methodist University, Department of Mathematics

Numerical solution of linear and nonlinear equations, interpolation and approximation of functions, numerical integration, floating-point arithmetic, and the numerical solution of initial value problems in ordinary differential equations. Student use of the computer is emphasized.

Math 5316 – Introduction to Matrix Computation

Undergraduate, Southern Methodist University, Department of Mathematics

The efficient solution of dense and sparse linear systems, least squares problems, and eigenvalue problems. Elementary and orthogonal matrix transformations provide a unified treatment. Programming is in MATLAB, with a focus on algorithms.

Math 6316 – Numerical Methods I

Graduate, Southern Methodist University, Department of Mathematics

The efficient solution of dense and sparse linear systems, least squares problems and eigenvalue problems. Elementary and orthogonal matrix transformations provide a unified treatment. In addition to algorithm development, the course emphasizes the theory underlying the methods.

Math 6317 – Numerical Methods II

Graduate, Southern Methodist University, Department of Mathematics

Covers interpolation and approximation of functions, numerical differentiation and integration, basic methods for initial value problems in ordinary differential equations, and basic approximation methods for one-dimensional initial-boundary value problems. Topics focus on algorithm development and the theory underlying each method.

Current courses

Southern Methodist University, Department of Mathematics, Fall 2024

Fall 2024: None (on sabbatical)