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ARKODE: A Flexible IVP Solver Infrastructure for One-step Methods

Journal Article · · ACM Transactions on Mathematical Software
DOI:https://doi.org/10.1145/3594632· OSTI ID:1991757
 [1];  [2];  [2];  [3]
  1. Southern Methodist University, Dallas, TX (United States); Southern Methodist University
  2. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
  3. Temple University, Philadelphia, PA (United States)
+ Show Author Affiliations
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.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Southern Methodist University, Dallas, TX (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC52-07NA27344; SC0021354
OSTI ID:
1991757
Alternate ID(s):
OSTI ID: 1999746
Report Number(s):
LLNL-JRNL--835429
Journal Information:
ACM Transactions on Mathematical Software, Journal Name: ACM Transactions on Mathematical Software Journal Issue: 2 Vol. 49; ISSN 0098-3500
Publisher:
Association for Computing MachineryCopyright Statement
Country of Publication:
United States
Language:
English

References (47)

Geometric Numerical Integration book January 2002
Multirate linear multistep methods journal December 1984
Multirate generalized additive Runge Kutta methods journal August 2015
Multirate infinitesimal step methods for atmospheric flow simulation journal April 2009
Implicit–Explicit Runge–Kutta Schemes and Applications to Hyperbolic Systems with Relaxation journal October 2005
Characterizing Strong Stability Preserving Additive Runge-Kutta Methods journal October 2008
Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales journal December 2012
Implicit Multirate GARK Methods journal February 2021
Phase Field Simulations of Autocatalytic Formation of Alpha Lamellar Colonies in Ti-6Al-4V journal September 2016
Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics journal November 2021
A 3(2) pair of Runge - Kutta formulas journal January 1989
Additive Runge–Kutta schemes for convection–diffusion–reaction equations journal January 2003
Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows journal October 1998
Modeling primordial gas in numerical cosmology journal August 1997
Numerical solution of multiscale problems in atmospheric modeling journal October 2012
Higher-order additive Runge–Kutta schemes for ordinary differential equations journal February 2019
A comparison of fourth-order operator splitting methods for cardiac simulations journal November 2019
Multirate Runge–Kutta schemes for advection equations journal April 2009
Optimized strong stability preserving IMEX Runge–Kutta methods journal December 2014
MFEM: A modular finite element methods library journal January 2021
Towards dense linear algebra for hybrid GPU accelerated manycore systems journal June 2010
Enabling GPU accelerated computing in the SUNDIALS time integration library journal December 2021
Evaluation of Implicit‐Explicit Additive Runge‐Kutta Integrators for the HOMME‐NH Dynamical Core journal December 2019
High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD journal March 2003
Calculated rates for the electron impact dissociation of molecular hydrogen, deuterium and tritium journal June 2002
Implicit integration methods for dislocation dynamics journal January 2015
Additive methods for the numerical solution of ordinary differential equations journal January 1980
Uncertainties in H 2 and HD chemistry and cooling and their role in early structure formation journal August 2008
Experimental Results for H 2 Formation from H − and H and Implications for First Star Formation journal July 2010
Strong Stability for Additive Runge–Kutta Methods journal January 2006
Parallel Time Integration with Multigrid journal January 2014
A Class of Multirate Infinitesimal GARK Methods journal January 2019
A New Class of High-Order Methods for Multirate Differential Equations journal January 2020
Coupled Multirate Infinitesimal GARK Schemes for Stiff Systems with Multiple Time Scales journal January 2020
Implicit-Explicit Multirate Infinitesimal GARK Methods journal January 2021
Adaptive Time Step Control for Multirate Infinitesimal Methods journal April 2023
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers journal September 2005
Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods journal December 1994
Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods journal December 1991
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers journal September 2022
Digital filters in adaptive time-stepping journal March 2003
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides journal September 1990
PeleC: An adaptive mesh refinement solver for compressible reacting flows journal September 2022
Multirate Partitioned Runge-Kutta Methods for Coupled Navier-Stokes Equations preprint January 2022
Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models journal January 2018
Implementation of multirate time integration methods for air pollution modelling journal November 2012
DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia journal May 2017

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Related Subjects

97 MATHEMATICS AND COMPUTING
Adaptive integration
Additive Runge-Kutta
IMEX methods
Multirate method
ODEs