## 2007

Alan C. Hindmarsh and Radu Serban (2007), “SUNDIALS Equation Solvers,” Scholarpedia, p. 10676.

## 2005

Radu Serban and Alan C. Hindmarsh, “CVODES: The Sensitivity-Enabled ODE Solver in SUNDIALS, Proceedings of IDETC/CIE 2005, ASME, Sept. 24-28, 2005, Long Beach, CA, USA. Also available as LLNL Technical Report UCRL-PROC-210300, March 2005 [PDF].

Alan C. Hindmarsh, Peter N. Brown, Keith E. Grant, Steven L. Lee, Radu Serban, Dan E. Shumaker, and Carol S. Woodward, " SUNDIALS: Suite of Nonlinear and Differential/Algebraic Equation Solvers,” *ACM Transactions on Mathematical Software*, 31 (3), Sept. 2005, pp. 363–396. Also available as LLNL Technical Report UCRL-JP-200037 [PDF].

Peter N. Brown, Dana E. Shumaker, and Carol S. Woodward, “Fully Implicit Solution of Large-Scale Non-Equilibrium Radiation Diffusion with High Order Time Integration,” to appear in *Journal on Computational Physics*. Also available as LLNL Technical Report UCRL-JRNL-203809 [PDF].

## 2004

Miller, D.S. and C.S. Woodward, “Exploring Nonlinear Couplings in Radiation Diffusion Problems,” Proceedings of the NECDC 2004. UCRL-CONF-155727.

Walker, Homer, and Carol S. Woodward, “Application Scientists Join Algorithm Designers at Workshop on Large-Scale Nonlinear Problems,” *SIAM News*, March 2004, 37 (2).

## 2003

Steven L. Lee, Carol S. Woodward, and Frank Graziani, “Analyzing Radiation Diffusion using Time-Dependent Sensitivity-Based Techniques,”*Journal of Computational Physics*, 192, (1), (2003), pp. 211–230. Also available as LLNL Technical Report UCRL-JC-152392 [PDF].

Peter N. Brown, Panayot Vassilevski, and Carol S. Woodward, “On Mesh-Independent Convergence of an Inexact Newton-Multigrid Algorithm,” *SIAM J. Sci. Comput.*, 25, (2) 2003, pp. 570–590. Also available as LLNL Technical Report UCRL-JC-148376 [PDF].

Jones, J.E., P.S. Vassilevski, and C.S. Woodward, “Nonlinear Schwarz-FAS Methods for Unstructured Finite Element Problems,” proceedings of Second M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, MA, June 17–20, 2003. Also Available as LLNL Technical Report UCRL-JC-150427.

## 2002

Dumett, M., P. Vassilevski, and C. S. Woodward, “A Multigrid Method for Nonlinear Unstructured Finite Element Elliptic Equations,” submitted (2002). Also available as LLNL Technical Report UCRL-JC-150513 [PDF].

Jim E. Jones, Panayot S. Vassilevski, and Carol S. Woodward, "Nonlinear Schwarz-FAS Methods for Unstructured Finite Element Problems,” submitted to *Second M.I.T. Conference on Computational Fluid and Solid Mechanics*, Cambridge, MA, June 17–20, 2003. Also available as LLNL Technical Report UCRL-JC-150427. [PDF].

Dumett, M., P. Vassilevski, and C. S. Woodward, “A Multigrid Method for Nonlinear Unstructured Finite Element Elliptic Equations,” (2002). Available as LLNL Technical Report UCRL-JC-150513.

Hindmarsh, Alan C. and Serban, Radu, “User Documentation for CVODES, An ODE Solver with Sensitivity Analysis Capabilities,” LLNL Technical Report UCRL-MA-148813, July 2002. [PDF].

Woodward, Carol S., Keith E. Grant, and Reed Maxwell, “Applications of Sensitivity Analysis to Uncertainty Quantification for Variably Saturated Flow,” S. M. Hassanizadeh, R. J. Schotting, W. G. Gray, and G. F. Pinder, Eds., Computational Methods in Water Resources, Vol. 1, Elsevier, Amsterdam, 2002, pp. 73–80. Available as LLNL Technical Report UCRL-JC-146976. [PDF].

## 2001

Brown, Peter N., Keith E. Grant, and Carol S. Woodward, “On the Calculation of Uncertainties for 3-D Time-Dependent Neutral Particle Transport,” submitted to *Journal of Computational Physics*, 2001. Also available as LLNL Technical Report UCRL-JC-146186, November 2001 [PDF].

Alan C. Hindmarsh, “The PVODE Trio: PVODE, KINSOL, and IDA,” UCRL-JC-145579, October 2001; presented at the ACTS Toolkit Workshop, Berkeley, October 2001 [PDF].

Jones, Jim E., and Carol S. Woodward, “Newton-Krylov-Multigrid Solvers for Large-Scale, Highly Heterogeneous, Variably Saturated Flow Problems,” *Advances in Water Resources*, 24, July 2001, pp. 763–774. Also available as LLNL Technical Report UCRL-JC-138618 [PDF].

Brown, Peter N., and Carol S. Woodward, “Preconditioning Strategies for Fully Implicit Radiation Diffusion With Material-Energy Transfer,” * SIAM J. Sci. Comput.*, 23 May 2001, pp. 499–516. Also available as LLNL Technical Report UCRL-JC-139087 [PDF].

Hovland, Paul, Steven Lee, Lois McInnes, Boyana Norris, and Barry Smith," Challenges and Opportunities in Using Automatic Differentiation with Object-Oriented Toolkits for Scientific Computing,” LLNL Technical Report UCRL-JC-143410, April 2001.

Walker, Homer and Carol S. Woodward," Solution Methods for Large-Scale Nonlinear Problems: An Evolving Research Area,” in *SIAM News*, April 2001, p. 16. Also available as LLNL Technical Report UCRL-MI-141913.

Brown, Peter N., Frank Graziani, Ivan Otero, and Carol S. Woodward, “Implicit Solution of Large-Scale Radiation Diffusion Problems, “Nuclear Explosives Code Developers’ Collaborations,” Oakland, CA, October 23–27, 2001. Also available as LLNL Technical Report UCRL-JC-141881, January 2001 [PDF].

Brown, P.N., K. E. Grant, and C. S. Woodward, “On the Calculation of Uncertainties for 3D Time-Dependent Neutral Particle Transport,” (2001). Available as LLNL Technical Report UCRL-JC-146186.

## 2000

Hindmarsh, Alan C., “The PVODE and IDA Algorithms,” LLNL Technical Report UCRL-ID-141558, December 2000 [PDF].

Alan C. Hindmarsh and Mark D. Rotter, “Using an ODE Solver for a Class of Integro-Differential Systems,” *J. Comput. Phys.* 168 (2001), pp. 267–285. Also available as LLNL Technical Report UCRL-JC-138647, April 2000 [PDF].

Jones, Jim E., and Carol S. Woodward, “Preconditioning Newton-Krylov Methods for Variably Saturated Flow,” Proc. VIII Int. Conf. Comput. Meth. Water Resources, Calgary, Alberta, Canada, June 25–29, 2000. L. R. Bentley, J. F. Sykes, C. Brebbia, W. Gray, G. F. Pinder, Eds., *Computational Methods in Water Resources*, Balkema, Rotterdam, 2000. Vol. 1, pp. 101–106. Also available as LLNL Technical Report UCRL-JC-137011, June 2000 [PDF].

Lee, Steven L., Alan C. Hindmarsh, and Peter N. Brown, “User Documentation for SensPVODE, a Variant of PVODE for Sensitivity Analysis,” LLNL Technical Report UCRL-MA-140211, August 2000 [PDF].

Lee, Steven L., and Paul D. Hovland, “Sensitivity Analysis Using Parallel ODE Solvers and Automatic Differentiation in C: SensPVODE and ADIC,” to appear in *Proc. Automatic Differentiation: From Simulation to Optimization*, June 19-23, 2000. Springer-Verlag, 2001, Ch. 26. p. 217. Also available as LLNL Technical Report UCRL-JC-137728, September 2000.

Rognlien, T. D., X. Q. Xu, and A. C. Hindmarsh, “Application of Parallel Implicit Methods to Edge-Plasma Numerical Simulations,” *J. Comput. Phys.*, to appear. Also available as LLNL Technical Report UCRL-JC-138518, April 2000 [PDF].

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. Numer. Anal.*, 37, (2000), pp. 701–724. Also available as LLNL Technical Report UCRL-JC-125567.

## 1999

Brown, Peter N., Britton Chang, Frank Graziani, and Carol S. Woodward, “Implicit Solution of Large-Scale Radiation-Material Energy Transfer Problems,” *Iterative Meth. Sci. Comput. IV*, Volume 5 of Series in Computational and Applied Mathematics, IMACS, New Brunswick, NJ, D. R. Kincaid, A. C. Elster, Eds., 1999. pp. 342–356. Also available as LLNL Technical Report UCRL-JC-132831, January 1999.

Byrne, George D., and Alan C. Hindmarsh, “PVODE, An ODE Solver for Parallel Computers,” *Int. J. High Perf. Comput. Apps.*, 13, (4), (1999), pp. 354–365. Also available as LLNL Technical Report UCRL-JC-132361 Rev. 1, May 1999 [PDF].

Hindmarsh, Alan C., and A. G. Taylor, “User Documentation for IDA, a Differential-Algebraic Equation Solver for Sequential and Parallel Computers,” LLNL Technical Manual UCRL-MA-136910, December 1999 [PDF].

## 1998

Brown, P. N., A. C. Hindmarsh, and L. R. Petzold, “Consistent Initial Condition Calculation for Differential-Algebraic Systems,” *SIAM J. Sci. Comput.*, 19, (1998), pp. 1495–1512. Also available as LLNL Technical Report UCRL-JC-122175 Rev. 1, June 1996 [PDF].

Byrne, G. D., and A. C. Hindmarsh, “User Documentation for PVODE, An ODE Solver for Parallel Computers,” LLNL Technical Report UCRL-ID-130884, May 1998 [PDF].

Dawson, C. N., M. F. Wheeler, and C. S. Woodward, “A Two-Grid Finite Difference Scheme for Nonlinear Parabolic Equations,” *SIAM J. Numer. Anal.*, 35, (2), (1998), pp. 435–452. Also available as LLNL Technical Report UCRL-JC-125599, October 1996.

Hindmarsh, A. C., and A. G. Taylor, “PVODE and KINSOL: Parallel Software for Differential and Nonlinear Systems,” LLNL Technical Report UCRL-ID-129739, February 1998 [PDF].

Taylor, Allan G., and Alan C. Hindmarsh, “User Documentation for KINSOL, A Nonlinear Solver for Sequential and Parallel Computers,” LLNL Technical Report UCRL-ID-131185, July 1998 [PDF].

Woodward, C. S., “A Newton-Krylov-Multigrid Solver for Variably Saturated Flow Problems,” *Proc. XII Int. Conf. Comput. Meth. Water Resources*, Crete, Greece, June 15–19, 1998. Computational Mechanics Publications, Southampton, UK, Vol. 2, pp. 606–616. Also available as LLNL Technical Report UCRL-JC-129371, June 1998.

## 1997

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,” *J. Comput. Geosci.*, 1, (1997), pp. 215–249.

## 1996

Cohen, S. D., and A. C. Hindmarsh, “CVODE, A Stiff/Nonstiff ODE Solver in C,” *Computers in Physics*, 10, (2), (March April 1996), pp. 138–143. Also available as LLNL Technical Report UCRL-JC-121014 Rev. 1, August 1995 [PDF].

Henson, Van Emden, and A. W. Shaker, “Theory and Numerics for a Semilinear Elliptic PDE, With an Application in the Theory of Pseudoplastic Fluids,” *Applicable Analysis*, 63, (1996), pp. 271–285.

Wittman, Michael R., “Testing of PVODE, a Parallel ODE Solver,” LLNL Technical Report UCRL-ID-125562, August 1996 [PDF].

## 1995

Henson, Van Emden, and A. Shaker, “Multigrid Solution of a Singular Nonlinear BVP in Fluid Theory,” *1st Asian Comput. Fluid. Dynam. Conf.*, Hong Kong University of Science and Technology, 1995. 2, pp. 791–796.

Hindmarsh, A. C., “Avoiding BDF Stability Barriers in the MOL Solution of Advection-Dominated Problems,” *Appl. Numer. Math.*, 17, (1995), pp. 311–318. Also available as LLNL Technical Report UCRL-JC-116618 Rev. 1, April 1994 [PDF].

Hindmarsh, A. C., and L. R. Petzold, “Algorithms and Software for Ordinary Differential Equations and Differential-Algebraic Equations,” *Computers in Physics*, 9, (1995), pp. 34–41 and 148–155. Also available as LLNL Technical Report UCRL-JC-116619, April 1994 [PDF].

## 1994

Brown, P. N., A. C. Hindmarsh, and L. R. Petzold, “Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems,” *SIAM J. Sci. Comput.*, 15, (1994), pp. 1467–1488. Also available as LLNL Technical Report UCRL-JC-113507, March 1993 [PDF].

Cohen, S. D., and A. C. Hindmarsh, “CVODE User Guide,” LLNL Technical Report UCRL-MA-118618, September 1994 [PDF].

## 1993

Radhakrishnan, Krishnan, and Alan C. Hindmarsh, “Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations,” NASA reference publication 1327. Also available as LLNL Technical Report UCRL-ID-113855, 1993 [PDF].

Henson, Van Emden, and A. Shaker, “Multigrid Methods for a Semilinear PDE in the Theory of Pseudoplastic Fluids,” *Proc. Copper Mt. Conf. Multigrid Meth.*, Copper Mountain, CO, 1993. pp. 231–342. NASA Conference Publications, CP-3224.

## 1992

A. C. Hindmarsh, “Detecting Stability Barriers in BDF Solvers,” in *Computational Ordinary Differential Equations*, J. R. Cash and I. Gladwell (eds.), Carendon Press, Oxford, 1992, pp. 87–96. Also UCRL-101197, June 1989 [PDF].

## 1989

P. N. Brown and A. C. Hindmarsh, “Reduced Storage Matrix Methods in Stiff ODE Systems,” *J. Appl. Math. & Comput.* 31 (1989), pp. 40–91. Also UCRL-95088 Rev. 1, June 1987 [PDF].

## 1988

A. C. Hindmarsh and S. P. Norsett, “KRYSI, An ODE Solver Combining a Semi-Implicit Runge-Kutta Method and a Preconditioned Krylov Method,” LLNL Report UCID-21422, May 1988. Also *Norges Tekniske Hogskole Mathematics of Computation Report*, August 1987, Trondheim, Norway [PDF].

## 1987

Hindmarsh, A. C., and P. N. Brown, “Reduced-Storage Techniques in the Numerical Method of Lines.” Also available as LLNL Technical Report UCRL-96261, February 1987 [PDF].

## 1986

Byrne, G.D., and A. C. Hindmarsh, “Stiff ODE Solvers: A Review of Current and Coming Attractions,” *J. Comp. Phys.* 70 (1987), pp. 1–62. Also available as LLNL Technical Report UCRL-94297, March 1986 [PDF].

## 1985

Brown, P. N., and A. C. Hindmarsh, “Matrix-Free Methods for Stiff Systems of ODEs,” *SIAM J. Numer. Anal.*, 23 (1986), 610-638. Also available as LLNL Technical Report UCRL-90770 Rev. 1, May 1985 [PDF].

## 1983

Alan C. Hindmarsh, “ODEPACK, A Systematized Collection of ODE Solvers,” in *Scientific Computing*, R. S. Stepleman et al., eds., North-Holland, Amsterdam, 1983, pp. 55–64. Also UCRL-88007, August 1982 [PDF].

## 1977

Alan C. Hindmarsh, “Solution of Block-Tridiagonal Systems of Linear Algebraic Equations,” LLNL report UCID-30150, February 1977 [PDF].

## 1976

A. C. Hindmarsh, “Preliminary Documentation of GEARBI: Solution of ODE Systems with Block-Iterative Treatment of the Jacobian,” LLNL report UCID-30149, December 1976 [PDF].