SUNDIALS was awarded the 2023 SIAM/ACM Prize in Computational Science and Engineering. Read more at LLNL News.

SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) is an open-source software library designed to provide a reliable tool for solving mathematical equations that are fundamental to modeling and simulating physical phenomena and can easily be incorporated into existing simulation codes. It consists of six packages: including methods for solving ordinary differential equation (ODE) systems, differential-algebraic equation (DAE) systems and nonlinear, algebraic systems. The time integrator packages include step and order adaptive linear multistep methods, step adaptive multistage Runge-Kutta methods, and most recently, multirate methods for systems with multiple separated time scales. The nonlinear solvers include Newton-based methods as well as Anderson-accelerated fixed point methods.

 
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SUNDIALS is a SUite of Nonlinear and DIfferential/ALgebraic equation Solvers:

CVODE
solves initial value problems for ordinary differential equation (ODE) systems

CVODES
solves ODE systems and includes sensitivity analysis capabilities (forward and adjoint).

ARKODE
solves initial value ODE problems with additive Runge-Kutta methods, including support for IMEX methods.

IDA
solves initial value problems for differential-algebraic equation (DAE) systems.

IDAS
solves DAE systems and includes sensitivity analysis capabilities (forward and adjoint).

KINSOL
solves nonlinear algebraic systems.

 

SUNDIALS is implemented with the goal of providing robust time integrators and nonlinear solvers that can easily be incorporated into existing simulation codes. The primary design goals are to require minimal information from the user, allow users to easily supply their own data structures underneath the packages, and allow for easy incorporation of user-supplied linear solvers and preconditioners.

The main numerical operations performed in these codes are linear algebra operations (norms, dot products, linear solves etc.), and the codes have been written in terms of these. The result of this design is that users can relatively easily provide their own vector and matrix (if applicable) data structures to the solvers by telling the solver about their structures and providing the required operations on them. All parallelism is contained within the linear algebra operations and problem defining functions provided by the user. No other operations within the packages require knowledge of parallelism. Hence, we do not make a distinction between parallel and serial versions of the codes.

SUNDIALS comes with several vector and matrix data structures as well as nonlinear and linear solver implementations that can be leveraged by users who do not wish to provide their own. These data structures and solvers span a wide range of computing paradigms including shared-memory and distributed memory parallelism and GPU computing. For more details on the six SUNDIALS packages, see the links in the table below.

Acknowledgments

SUNDIALS is based on work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program via the Frameworks, Algorithms, and Scalable Technologies for Mathematics (FASTMath) Institute under DOE awards DE-AC52-07NA27344 and DE-SC-0021354. SUNDIALS is also based on work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Next-Generation Scientific Software Technologies program under contract DE-AC52-07NA27344. Additional support is also provided by SciDAC partnerships with the U.S. Department of Energy’s FES, NP, BES, OE, and BER offices as well as the LLNL Institutional Scientific Capability Portfolio.