Journal
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
Volume 49, Issue 2, Pages -Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3594632
Keywords
ODEs; adaptive integration; additive Runge-Kutta methods; ImEx methods; multirate methods
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We introduce the ARKODE library, which contains one-step time integration methods for ordinary differential equation initial-value problems. It not only includes standard explicit and diagonally implicit Runge-Kutta methods, but also supports one-step methods for additive splittings of the IVP, such as implicit-explicit additive Runge-Kutta methods and multirate infinitesimal methods.
We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge-Kutta methods, ARKODE supports one-step methods designed to treat additive splittings of the IVP, including implicit-explicit (ImEx) additive Runge-Kutta methods and multirate infinitesimal (MRI) methods. We present the role of ARKODE within the SUNDIALS suite of time integration and nonlinear solver libraries, the core ARKODE infrastructure for utilities common to large classes of one-step methods, as well as its use of time stepper modules enabling easy incorporation of novel algorithms into the library. Numerical results show example problems of increasing complexity, highlighting the algorithmic flexibility afforded through this infrastructure, and include a larger multiphysics application leveraging multiple algorithmic features from ARKODE and SUNDIALS.
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