Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

Fekete, Imre; Conde, Sidafa; Shadid, John N.

doi:10.1016/j.cam.2022.114325

Title: Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

Journal Article · Thu Apr 14 00:00:00 EDT 2022 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2022.114325· OSTI ID:1870469

^[1]; Conde, Sidafa ^[2]; Shadid, John N. ^[3]

Eötvös Loránd University (Hungary); MTA-ELTE Numerical Analysis and Large Networks Research Group (Hungary)
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States); Univ. of New Mexico, Albuquerque, NM (United States)

We construct a family of embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods of order 2 ≤ p ≤ 4 to be used to obtain numerical solution of spatially discretized hyperbolic PDEs. In this construction, the goals include non-defective property, large stability region, and small error values as defined in Dekker and Verwer (1984) and Kennedy et al. (2000). The new family of embedded pairs offer the ability for strong stability preserving (SSP) methods to adapt by varying the step-size. Through several numerical experiments, we assess the overall effectiveness in terms of work versus precision while also taking into consideration accuracy and stability.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1870469

Report Number(s):: SAND2022-3682J; 704754

Journal Information:: Journal of Computational and Applied Mathematics, Vol. 412; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (19)

A family of embedded Runge-Kutta formulae Dormand, J. R.; Prince, P. J. Journal of Computational and Applied Mathematics, Vol. 6, Issue 1 https://doi.org/10.1016/0771-050X(80)90013-3	journal	March 1980
XSEDE: Accelerating Scientific Discovery Towns, John; Cockerill, Timothy; Dahan, Maytal Computing in Science & Engineering, Vol. 16, Issue 5 https://doi.org/10.1109/MCSE.2014.80	journal	September 2014
Digital filters in adaptive time-stepping Söderlind, Gustaf ACM Transactions on Mathematical Software, Vol. 29, Issue 1 https://doi.org/10.1145/641876.641877	journal	March 2003
Contractivity of Runge-Kutta methods Kraaijevanger, J. F. B. M. BIT, Vol. 31, Issue 3 https://doi.org/10.1007/BF01933264	journal	September 1991
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods Spiteri, Raymond J.; Ruuth, Steven J. SIAM Journal on Numerical Analysis, Vol. 40, Issue 2 https://doi.org/10.1137/S0036142901389025	journal	January 2002
Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations Ketcheson, David I. SIAM Journal on Scientific Computing, Vol. 30, Issue 4 https://doi.org/10.1137/07070485X	journal	January 2008
Total-Variation-Diminishing Time Discretizations Shu, Chi-Wang SIAM Journal on Scientific and Statistical Computing, Vol. 9, Issue 6 https://doi.org/10.1137/0909073	journal	November 1988
On Strong Stability Preserving Time Discretization Methods Higueras, Inmaculada Journal of Scientific Computing, Vol. 21, Issue 2 https://doi.org/10.1023/B:JOMP.0000030075.59237.61	journal	October 2004
Stability radius of polynomials occurring in the numerical solution of initial value problems van der Marel, Roeland P. BIT Numerical Mathematics, Vol. 30, Issue 3 https://doi.org/10.1007/BF01931665	journal	September 1990
Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order Conde, Sidafa; Gottlieb, Sigal; Grant, Zachary J. Journal of Scientific Computing, Vol. 73, Issue 2-3 https://doi.org/10.1007/s10915-017-0560-2	journal	September 2017
Time-step selection algorithms: Adaptivity, control, and signal processing Söderlind, Gustaf Applied Numerical Mathematics, Vol. 56, Issue 3-4 https://doi.org/10.1016/j.apnum.2005.04.026	journal	March 2006
A 3(2) pair of Runge - Kutta formulas Bogacki, P.; Shampine, L. F. Applied Mathematics Letters, Vol. 2, Issue 4 https://doi.org/10.1016/0893-9659(89)90079-7	journal	January 1989
Additive Runge–Kutta schemes for convection–diffusion–reaction equations Kennedy, Christopher A.; Carpenter, Mark H. Applied Numerical Mathematics, Vol. 44, Issue 1-2 https://doi.org/10.1016/S0168-9274(02)00138-1	journal	January 2003
Efficient implementation of essentially non-oscillatory shock-capturing schemes Shu, Chi-Wang; Osher, Stanley Journal of Computational Physics, Vol. 77, Issue 2 https://doi.org/10.1016/0021-9991(88)90177-5	journal	August 1988
Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations Kennedy, Christopher A.; Carpenter, Mark H.; Lewis, R. Michael Applied Numerical Mathematics, Vol. 35, Issue 3 https://doi.org/10.1016/S0168-9274(99)00141-5	journal	November 2000
Efficient Implementation of Weighted ENO Schemes Jiang, Guang-Shan; Shu, Chi-Wang Journal of Computational Physics, Vol. 126, Issue 1 https://doi.org/10.1006/jcph.1996.0130	journal	June 1996
Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods Gustafsson, Kjell ACM Transactions on Mathematical Software, Vol. 17, Issue 4 https://doi.org/10.1145/210232.210242	journal	December 1991
Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel Mathematics of Computation, Vol. 84, Issue 296 https://doi.org/10.1090/mcom/2966	journal	April 2015
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089020	journal	September 2005

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Title: Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods

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