17. Bibliography


Xbraid: parallel multigrid in time. http://llnl.gov/casc/xbraid.


AMD ROCm Documentation. https://rocmdocs.amd.com/en/latest/index.html.


KLU Sparse Matrix Factorization Library. http://faculty.cse.tamu.edu/davis/suitesparse.html.


NVIDIA CUDA Programming Guide. https://docs.nvidia.com/cuda/index.html.


NVIDIA cuSOLVER Programming Guide. https://docs.nvidia.com/cuda/cusolver/index.html.


NVIDIA cuSPARSE Programming Guide. https://docs.nvidia.com/cuda/cusparse/index.html.


SuperLU_DIST Parallel Sparse Matrix Factorization Library. https://portal.nersc.gov/project/sparse/superlu/#superlu_dist.


SuperLU_MT Threaded Sparse Matrix Factorization Library. https://portal.nersc.gov/project/sparse/superlu/#superlu_mt.


Kasia Świrydowicz, Julien Langou, Shreyas Ananthan, Ulrike Yang, and Stephen Thomas. Low synchronization gram-schmidt and gmres algorithms. Numerical Linear Algebra with Applications, 28(2):e2343, Oct 2021. doi:10.1002/nla.2343.


D. G. Anderson. Iterative procedures for nonlinear integral equations. J. Assoc. Comput. Machinery, 12:547–560, 1965. doi:10.1145/321296.321305.


Hartwig Anzt, Terry Cojean, Goran Flegar, Fritz Göbel, Thomas Grützmacher, Pratik Nayak, Tobias Ribizel, Yuhsiang Mike Tsai, and Enrique S. Quintana-Ortí. Ginkgo: A Modern Linear Operator Algebra Framework for High Performance Computing. ACM Transactions on Mathematical Software, 48(1):2:1–2:33, February 2022. URL: https://doi.org/10.1145/3480935 (visited on 2022-02-17), doi:10.1145/3480935.


U. M. Ascher and L. R. Petzold. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM, Philadelphia, Pa, 1998.


Cody J Balos, David J Gardner, Carol S Woodward, and Daniel R Reynolds. Enabling GPU accelerated computing in the SUNDIALS time integration library. Parallel Computing, 108:102836, 2021. doi:10.1016/j.parco.2021.102836.


R.E. Bank, W.M. Coughran, W. Fichtner, E.H. Grosse, D.J. Rose, and R.K. Smith. Transient simulation of silicon devices and circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 4(4):436–451, 1985. doi:10.1109/TCAD.1985.1270142.


S.R Billington. Type-insensitive codes for the solution of stiff and nonstiff systems of ordinary differential equations. Master Thesis, University of Manchester, United Kingdom, 1983.


David Boehme, Todd Gamblin, David Beckingsale, Peer-Timo Bremer, Alfredo Gimenez, Matthew LeGendre, Olga Pearce, and Martin Schulz. Caliper: performance introspection for hpc software stacks. In SC'16: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 550–560. IEEE, 2016. doi:10.1109/SC.2016.46.


P. Bogacki and L.F. Shampine. A 3(2) pair of Runge-Kutta formulas. Applied Mathematics Letters, 2(4):321–325, 1989. doi:10.1016/0893-9659(89)90079-7.


K. E. Brenan, S. L. Campbell, and L. R. Petzold. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia, Pa, 1996. doi:10.1137/1.9781611971224.


P. N. Brown. A local convergence theory for combined inexact-Newton/finite difference projection methods. SIAM J. Numer. Anal., 24(2):407–434, 1987. doi:10.1137/0724031.


P. N. Brown, G. D. Byrne, and A. C. Hindmarsh. VODE, a Variable-Coefficient ODE Solver. SIAM J. Sci. Stat. Comput., 10:1038–1051, 1989. doi:10.1137/0910062.


P. N. Brown and A. C. Hindmarsh. Reduced storage matrix methods in stiff ODE systems. J. Appl. Math. & Comp., 31:49–91, 1989. doi:10.1016/0096-3003(89)90110-0.


P. N. Brown, A. C. Hindmarsh, and L. R. Petzold. Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems. SIAM J. Sci. Comput., 15:1467–1488, 1994. doi:10.1137/0915088.


P. N. Brown, A. C. Hindmarsh, and L. R. Petzold. Consistent Initial Condition Calculation for Differential-Algebraic Systems. SIAM J. Sci. Comput., 19:1495–1512, 1998. doi:10.1137/S1064827595289996.


P. N. Brown and Y. Saad. Hybrid Krylov Methods for Nonlinear Systems of Equations. SIAM J. Sci. Stat. Comput., 11:450–481, 1990. doi:10.1137/0911026.


J.C. Butcher. Numerical Methods for Ordinary Differential Equations. Wiley, Chicester, England, 2 edition, 2008.


G. D. Byrne. Pragmatic Experiments with Krylov Methods in the Stiff ODE Setting. In J.R. Cash and I. Gladwell, editors, Computational Ordinary Differential Equations, 323–356. Oxford, 1992. Oxford University Press.


G. D. Byrne and A. C. Hindmarsh. A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations. ACM Trans. Math. Softw., 1:71–96, 1975. doi:10.1145/355626.355636.


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


G. D. Byrne and A. C. Hindmarsh. PVODE, an ODE Solver for Parallel Computers. Intl. J. High Perf. Comput. Apps., 13(4):254–365, 1999. doi:10.1177/109434209901300405.


J Candy and W Rozmus. A symplectic integration algorithm for separable hamiltonian functions. Journal of Computational Physics, 92(1):230–256, 1991.


Y. Cao, S. Li, L. R. Petzold, and R. Serban. Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and its Numerical Solution. SIAM J. Sci. Comput., 24(3):1076–1089, 2003. doi:10.1137/S1064827501380630.


M. Caracotsios and W. E. Stewart. Sensitivity analysis of initial value problems with mixed odes and algebraic equations. Computers and Chemical Engineering, 9(4):359–365, 1985. doi:10.1016/0098-1354(85)85014-6.


J.R. Cash. Diagonally Implicit Runge-Kutta Formulae with Error Estimates. IMA Journal of Applied Mathematics, 24(3):293–301, 1979. doi:10.1093/imamat/24.3.293.


J.R. Cash and A.H. Karp. A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides. ACM Transactions on Mathematical Software, 16(3):201–222, 1990. doi:10.1145/79505.79507.


Rujeko Chinomona and Daniel R Reynolds. Implicit-explicit multirate infinitesimal GARK methods. SIAM Journal on Scientific Computing, 43(5):A3082–A3113, 2021. doi:10.1137/20M1354349.


S. D. Cohen and A. C. Hindmarsh. CVODE User Guide. Technical Report UCRL-MA-118618, LLNL, Sep 1994.


S. D. Cohen and A. C. Hindmarsh. CVODE, A Stiff/Nonstiff ODE Solver in C. Computers in Physics, 10(2):138–143, 1996. doi:10.1063/1.4822377.


Aaron M. Collier and Radu Serban. Example Programs for KINSOL v7.0.0. Technical Report UCRL-SM-208114, LLNL, 2024.


T. A. Davis and P. N. Ekanathan. Algorithm 907: KLU, a direct sparse solver for circuit simulation problems. ACM Trans. Math. Softw., 37(3):1–17, 2010. doi:10.1145/1824801.1824814.


R. S. Dembo, S. C. Eisenstat, and T. Steihaug. Inexact Newton Methods. SIAM J. Numer. Anal., 19(2):400–408, 1982. doi:10.1137/0719025.


J. W. Demmel, J. R. Gilbert, and X. S. Li. An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination. SIAM J. Matrix Analysis and Applications, 20(4):915–952, 1999. doi:10.1137/S0895479897317685.


J. E. Dennis and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia, 1996. doi:10.1137/1.9781611971200.


Fasma Diele and Carmela Marangi. Explicit symplectic partitioned Runge–Kutta–Nyström methods for non-autonomous dynamics. Applied Numerical Mathematics, 61(7):832–843, 2011. doi:10.1016/j.apnum.2011.02.003.


J.R. Dormand and P.J. Prince. A family of embedded runge-kutta formulae. Journal of Computational and Applied Mathematics, 6(1):19–26, 1980. doi:10.1016/0771-050X(80)90013-3.


M.R. Dorr, J.-L. Fattebert, M.E. Wickett, J.F. Belak, and P.E.A. Turchi. A numerical algorithm for the solution of a phase-field model of polycrystalline materials. Journal of Computational Physics, 229(3):626–641, 2010. doi:10.1016/j.jcp.2009.09.041.


H. Carter Edwards, Christian R. Trott, and Daniel Sunderland. Kokkos: enabling manycore performance portability through polymorphic memory access patterns. Journal of Parallel and Distributed Computing, 74(12):3202–3216, 2014. doi:10.1016/j.jpdc.2014.07.003.


Edda Eich. Convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints. SIAM Journal on Numerical Analysis, 30(5):1467–1482, 1993. doi:10.1137/0730076.


S. C. Eisenstat and H. F. Walker. Choosing the Forcing Terms in an Inexact Newton Method. SIAM J. Sci. Comput., 17(1):16–32, 1996. doi:10.1137/0917003.


R.D. Falgout, S. Friedhoff, TZ.V. Kolev, S.P. MacLachlan, and J.B. Schroder. Parallel time integration with multigrid. SIAM Journal of Scientific Computing, 36(6):C635–C661, 2014. doi:10.1137/130944230.


H. Fang and Y. Saad. Two classes of secant methods for nonlinear acceleration. Numer. Linear Algebra Appl., 16(3):197–221, 2009. doi:10.1002/nla.617.


W. F. Feehery, J. E. Tolsma, and P. I. Barton. Efficient Sensitivity Analysis of Large-Scale Differential-Algebraic Systems. Applied Numer. Math., 25(1):41–54, 1997. doi:10.1016/S0168-9274(97)00050-0.


E. Fehlberg. Low-order classical runge-kutta formulas with step size control and their application to some heat transfer problems. Technical Report 315, NASA, 1969.


Imre Fekete, Sidafa Conde, and John N. Shadid. Embedded pairs for optimal explicit strong stability preserving Runge–Kutta methods. Journal of Computational and Applied Mathematics, 412:114325, 2022. doi:10.1016/j.cam.2022.114325.


R. W. Freund. A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems. SIAM J. Sci. Comp., 14(2):470–482, 1993. doi:10.1137/0914029.


F. X. Giraldo, J. F. Kelly, and E. M. Constantinescu. Implicit-explicit formulations of a three-dimensional nonhydrostatic unified model of the atmosphere (numa). SIAM Journal on Scientific Computing, 35(5):B1162–B1194, 2013. doi:10.1137/120876034.


Laura Grigori, James W. Demmel, and Xiaoye S. Li. Parallel symbolic factorization for sparse LU with static pivoting. SIAM J. Scientific Computing, 29(3):1289–1314, 2007. doi:10.1137/050638102.


K. Gustafsson. Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods. ACM Transactions on Mathematical Software, 17(4):533–554, 1991. doi:10.1145/210232.210242.


K. Gustafsson. Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods. ACM Transactions on Mathematical Software, 20(4):496–512, 1994. doi:10.1145/198429.198437.


E. Hairer, S. P. Norsett, and G. Wanner. Solving Ordinary Differential Equations I. Springer-Verlag, Berlin, 1987.


E. Hairer and G. Wanner. Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin, 1991.


Ernst Hairer, Gerhard Wanner, and Christian Lubich. Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics, 2006. doi:10.1007/3-540-30666-8.


Vicente Hernández, José E Román, and Andrés Tomás. A parallel variant of the gram-schmidt process with reorthogonalization. In PARCO, 221–228. 2005.


M. R. Hestenes and E. Stiefel. Methods of Conjugate Gradients for Solving Linear Systems. J. Research of the National Bureau of Standards, 49(6):409–436, 1952. doi:10.6028/jres.049.044.


K. L. Hiebert and L. F. Shampine. Implicitly Defined Output Points for Solutions of ODEs. Technical Report SAND80-0180, Sandia National Laboratories, February 1980.


A. C. Hindmarsh. Detecting Stability Barriers in BDF Solvers. In J.R. Cash and I. Gladwell, editor, Computational Ordinary Differential Equations, 87–96. Oxford, 1992. Oxford University Press.


A. C. Hindmarsh. Avoiding BDF stability barriers in the MOL solution of advection-dominated problems. Appl. Num. Math., 17(3):311–318, 1995. doi:10.1016/0168-9274(95)00036-T.


A. C. Hindmarsh. The PVODE and IDA Algorithms. Technical Report UCRL-ID-141558, LLNL, Dec 2000.


A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward. SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw., pages 363–396, 2005. doi:10.1145/1089014.1089020.


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


Alan C. Hindmarsh and Radu Serban. Example Programs for CVODE v7.0.0. Technical Report, LLNL, 2024. UCRL-SM-208110.


Alan C. Hindmarsh, Radu Serban, Cody J. Balos, David J. Gardner, Daniel R. Reynolds, and Carol S. Woodward. User Documentation for CVODE v7.0.0. Technical Report UCRL-SM-208108, LLNL, 2024.


Alan C. Hindmarsh, Radu Serban, Cody J. Balos, David J. Gardner, Daniel R. Reynolds, and Carol S. Woodward. User Documentation for KINSOL v7.0.0. Technical Report UCRL-SM-208116, LLNL, 2024.


Alan C. Hindmarsh, Radu Serban, and Aaron Collier. Example Programs for IDA v7.0.0. Technical Report UCRL-SM-208113, LLNL, 2024.


K. R. Jackson and R. Sacks-Davis. An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs. ACM Trans. Math. Softw., 6(3):295–318, 1980. doi:10.1145/355900.355903.


Laurent O Jay. Symplecticness conditions of some low order partitioned methods for non-autonomous hamiltonian systems. Numerical Algorithms, 86(2):495–514, 2021.


Seth R. Johnson, Andrey Prokopenko, and Katherine J. Evans. Automated fortran-c++ bindings for large-scale scientific applications. Computing in Science & Engineering, 22(5):84–94, 2020. doi:10.1109/MCSE.2019.2924204.


Shinhoo Kang and Emil M Constantinescu. Entropy–Preserving and Entropy–Stable Relaxation IMEX and Multirate Time–Stepping Methods. Journal of Scientific Computing, 93(1):1–31, 2022. doi:10.1007/s10915-022-01982-w.


C. T. Kelley. Iterative Methods for Solving Linear and Nonlinear Equations. SIAM, Philadelphia, 1995. doi:10.1137/1.9781611970944.


C.A. Kennedy and M.H. Carpenter. Additive runge-kutta schemes for convection-diffusion-reaction equations. Applied Numerical Mathematics, 44(1-2):139–181, 2003. doi:10.1016/S0168-9274(02)00138-1.


C.A. Kennedy and M.H. Carpenter. Diagonally implicit Runge–Kutta methods for ordinary differential equations. a review. Technical Report TM-2016-219173, NASA, 2016.


C.A. Kennedy and M.H. Carpenter. Diagonally implicit Runge–Kutta methods for stiff ODEs. Applied Numerical Mathematics, 146():221–244, 2019. doi:10.1016/j.apnum.2019.07.008.


C.A. Kennedy and M.H. Carpenter. Higher-order additive runge-kutta schemes for ordinary differential equations. Applied Numerical Mathematics, 136:183–205, 2019. doi:10.1016/j.apnum.2018.10.007.


David I Ketcheson. Relaxation Runge–Kutta methods: Conservation and stability for inner-product norms. SIAM Journal on Numerical Analysis, 57(6):2850–2870, 2019. doi:10.1137/19M1263662.


O. Knoth and R. Wolke. Implicit-explicit runge–kutta methods for computiong atmospheric reactive flows. Applied Numerical Analysis, 28(2-4):327–341, 1998. doi:10.1016/S0168-9274(98)00051-8.


A. Kværno. Singly Diagonally Implicit Runge-Kutta Methods with an Explicit First Stage. BIT Numerical Mathematics, 44:489–502, 2004. doi:10.1023/B:BITN.0000046811.70614.38.


S. Li, L. R. Petzold, and W. Zhu. Sensitivity Analysis of Differential-Algebraic Equations: A Comparison of Methods on a Special Problem. Applied Num. Math., 32(2):161–174, 2000. doi:10.1016/S0168-9274(99)00020-3.


X. S. Li. An overview of SuperLU: algorithms, implementation, and user interface. ACM Trans. Math. Softw., 31(3):302–325, September 2005. doi:10.1145/1089014.1089017.


X.S. Li, J.W. Demmel, J.R. Gilbert, L. Grigori, M. Shao, and I. Yamazaki. SuperLU Users' Guide. Technical Report LBNL-44289, Lawrence Berkeley National Laboratory, September 1999. http://crd.lbl.gov/ xiaoye/SuperLU/. Last update: August 2011.


Xiaoye S. Li and James W. Demmel. SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Trans. Mathematical Software, 29(2):110–140, June 2003. doi:10.1145/779359.779361.


P. A. Lott, H. F. Walker, C. S. Woodward, and U. M. Yang. An accelerated Picard method for nonlinear systems related to variably saturated flow. Adv. Wat. Resour., 38:92–101, 2012. doi:10.1016/j.advwatres.2011.12.013.


T. Maly and L. R. Petzold. Numerical Methods and Software for Sensitivity Analysis of Differential-Algebraic Systems. Applied Numerical Mathematics, 20(1-2):57–79, 1996. doi:10.1016/0168-9274(95)00117-4.


Robert I Mclachlan and Pau Atela. The accuracy of symplectic integrators. Nonlinearity, 5(2):541, 1992.


J. M. Ortega and W. C. Rheinbolt. Iterative solution of nonlinear equations in several variables. SIAM, Philadelphia, 2000. Originally published in 1970 by Academic Press. doi:10.1137/1.9780898719468.


D.B. Ozyurt and P.I. Barton. Cheap second order directional derivatives of stiff ODE embedded functionals. SIAM J. of Sci. Comp., 26(5):1725–1743, 2005. doi:10.1137/030601582.


K. Radhakrishnan and A. C. Hindmarsh. Description and Use of LSODE, the Livermore Solver for Ordinary Differential Equations. Technical Report UCRL-ID-113855, LLNL, march 1994.


Hendrik Ranocha and David I Ketcheson. Relaxation Runge–Kutta methods for Hamiltonian problems. Journal of Scientific Computing, 84(1):1–27, 2020. doi:10.1007/s10915-020-01277-y.


Hendrik Ranocha, Mohammed Sayyari, Lisandro Dalcin, Matteo Parsani, and David I Ketcheson. Relaxation Runge–Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier–Stokes Equations. SIAM Journal on Scientific Computing, 42(2):A612–A638, 2020. doi:10.1137/19M1263480.


Daniel R. Reynolds. Example Programs for ARKODE v6.0.0. Technical Report, Southern Methodist University, 2024.


Ronald D Ruth. A canonical integration technique. IEEE Trans. Nucl. Sci., 30(CERN-LEP-TH-83-14):2669–2671, 1983.


Y. Saad. A flexible inner-outer preconditioned GMRES algorithm. SIAM J. Sci. Comput., 14(2):461–469, 1993. doi:10.1137/0914028.


Y. Saad and M. H. Schultz. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems. SIAM J. Sci. Stat. Comp., 7(3):856–869, 1986. doi:10.1137/0907058.


A. Sandu. A class of multirate infinitesimal gark methods. SIAM Journal of Numerical Analysis, 57(5):2300–2327, 2019. doi:10.1137/18M1205492.


A. Sayfy and A. Aburub. Embedded Additive Runge-Kutta Methods. International Journal of Computer Mathematics, 79(8):945–953, 2002. doi:10.1080/00207160212109.


M. Schlegel, O. Knoth, M. Arnold, and R. Wolke. Multirate Runge–Kutta schemes for advection equations. Journal of Computational Applied Mathematics, 226(2):345–357, 2009. doi:10.1016/j.cam.2008.08.009.


M. Schlegel, O. Knoth, M. Arnold, and R. Wolke. Implementation of multirate time integration methods for air pollution modelling. GMD, 5(6):1395–1405, 2012. doi:10.5194/gmd-5-1395-2012.


M. Schlegel, O. Knoth, M. Arnold, and R. Wolke. Numerical solution of multiscale problems in atmospheric modeling. Applied Numerical Mathematics, 62(10):1531–1542, 2012. doi:10.1016/j.apnum.2012.06.023.


R. Serban and A. C. Hindmarsh. CVODES: The sensitivity-enabled ODE solver in SUNDIALS. In Proceedings of the 5th International Conference on Multibody Systems, Nonlinear Dynamics and Control. Long Beach, CA, 2005. ASME. doi:10.1115/DETC2005-85597.


Radu Serban and Alan C. Hindmarsh. Example Programs for CVODES v7.0.0. Technical Report UCRL-SM-208115, LLNL, 2024.


L. F. Shampine. Implementation of implicit formulas for the solution of ODEs. SIAM Journal on Scientific and Statistical Computing, 1(1):103–118, 1980. doi:10.1137/0901005.


LF Shampine. Conservation laws and the numerical solution of ODEs, II. Computers & Mathematics with Applications, 38(2):61–72, 1999. doi:10.1016/S0898-1221(99)00183-2.


Chi-Wang Shu and Stanley Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics, 77(2):439–471, 1988. doi:10.1016/0021-9991(88)90177-5.


G. Soderlind. The automatic control of numerical integration. CWI Quarterly, 11:55–74, 1998.


G. Soderlind. Digital filters in adaptive time-stepping. ACM Transactions on Mathematical Software, 29(1):1–26, 2003. doi:10.1145/641876.641877.


G. Soderlind. Time-step selection algorithms: Adaptivity, control and signal processing. Applied Numerical Mathematics, 56(3-4):488–502, 2006. doi:10.1016/j.apnum.2005.04.026.


M. Sofroniou and G. Spaletta. Construction of explicit Runge-Kutta pairs with stiffness detection. Mathematical and Computer Modelling, 40(11):1157–1169, 2004. doi:10.1016/j.mcm.2005.01.010.


Mark Sofroniou and Giulia Spaletta. Symplectic Methods for Separable Hamiltonian Systems. Lecture Notes in Computer Science, pages 506–515, 2002. doi:10.1007/3-540-47789-6\_53.


Mark Sofroniou and Giulia Spaletta. Derivation of symmetric composition constants for symmetric integrators. Optimization Methods and Software, 20(4-5):597–613, 2005.


Jürgen Struckmeier and Claus Riedel. Canonical transformations and exact invariants for time-dependent hamiltonian systems. Annalen der Physik, 11(1):15–38, 2002.


M Suzuki and K Umeno. Higher-order decomposition theory of exponential operators and its applications to qmc and nonlinear dynamics. Computer simulation studies in condensed-matter physics VI, pages 74–86, 1993.


Molei Tao and Shi Jin. Accurate and efficient simulations of hamiltonian mechanical systems with discontinuous potentials. Journal of Computational Physics, 450:110846, 2022. URL: https://www.sciencedirect.com/science/article/pii/S0021999121007415, doi:https://doi.org/10.1016/j.jcp.2021.110846.


Stanimire Tomov, Jack Dongarra, and Marc Baboulin. Towards dense linear algebra for hybrid GPU accelerated manycore systems. Parallel Computing, 36(5-6):232–240, June 2010. doi:10.1016/j.parco.2009.12.005.


Christian Trott, Luc Berger-Vergiat, David Poliakoff, Sivasankaran Rajamanickam, Damien Lebrun-Grandie, Jonathan Madsen, Nader Al Awar, Milos Gligoric, Galen Shipman, and Geoff Womeldorff. The kokkos ecosystem: comprehensive performance portability for high performance computing. Computing in Science Engineering, 23(5):10–18, 2021. doi:10.1109/MCSE.2021.3098509.


Christian R. Trott, Damien Lebrun-Grandié, Daniel Arndt, Jan Ciesko, Vinh Dang, Nathan Ellingwood, Rahulkumar Gayatri, Evan Harvey, Daisy S. Hollman, Dan Ibanez, Nevin Liber, Jonathan Madsen, Jeff Miles, David Poliakoff, Amy Powell, Sivasankaran Rajamanickam, Mikael Simberg, Dan Sunderland, Bruno Turcksin, and Jeremiah Wilke. Kokkos 3: programming model extensions for the exascale era. IEEE Transactions on Parallel and Distributed Systems, 33(4):805–817, 2022. doi:10.1109/TPDS.2021.3097283.


J.H Verner. Explicit runge-kutta methods with estimates of the local truncation error. SIAM Journal of Numerical Analysis, 15(4):772–790, 1978. doi:10.1137/0715051.


J.H Verner. Numerically optimal Runge–Kutta pairs with interpolants. Numerical Algorithms, 53(2):383–396, 2010. doi:10.1007/s11075-009-9290-3.


H. A. Van Der Vorst. Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems. SIAM J. Sci. Stat. Comp., 13(2):631–644, 1992. doi:10.1137/0913035.


H. F. Walker and P. Ni. Anderson Acceleration for Fixed-Point Iterations. SIAM Jour. Num. Anal., 49(4):1715–1735, 2011. doi:10.1137/10078356X.


Haruo Yoshida. Construction of higher order symplectic integrators. Physics letters A, 150(5-7):262–268, 1990.


J.A. Zonneveld. Automatic integration of ordinary differential equations. Technical Report R743, Mathematisch Centrum, Postbus 4079, 1009AB Amsterdam, 1963.