zbMATH — the first resource for mathematics

Parallel-in-Time Magnus integrators. (English) Zbl 1436.65208
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
65L05 Numerical methods for initial value problems
65Y05 Parallel numerical computation
Full Text: DOI
[1] S. Blanes, F. Casas, J. A. Oteo, and J. Ros, The Magnus expansion and some of its applications, Phys. Rep., 470 (2009), pp. 151–238.
[2] S. Blanes, F. Casas, and J. Ros, Improved high order integrators based on the Magnus expansion, BIT, 40 (2000), pp. 434–450.
[3] S. Blanes and P. C. Moan, Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems, Appl. Numer. Math., 56 (2006), pp. 1519–1537. · Zbl 1103.65129
[4] K. Burrage, Parallel methods for ODEs, Adv. Comput. Math., 7 (1997), pp. 1–3. · Zbl 0900.65210
[5] L. Euler, Institutiones calculi integralis, v. 2, Academiae Imperialis Scientiarum, 1768.
[6] M. J. Gander, 50 years of time parallel time integration, in Multiple Shooting and Time Domain Decomposition Methods, T. Carraro, M. Geiger, S. Körkel, and R. Rannacher, eds., Springer, Berlin, 2015, pp. 69–113. · Zbl 1337.65127
[7] E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, Berlin, 2006. · Zbl 1094.65125
[8] E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Math. Comput. Simul. 29, Springer, Berlin, 1987.
[9] E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer, Berlin, 1991. · Zbl 0729.65051
[10] N. J. Higham, The Scaling and Squaring Method for the Matrix Exponential Revisited, SIAM J. Matrix Anal. Appl., 26 (2005), pp. 1179–1193. · Zbl 1081.65037
[11] M. Hochbruck and A. Ostermann, Exponential integrators, Acta Numer., 19 (2010), pp. 209–286.
[12] A. Iserles, H. Z. Munthe-Kaas, S. P. Nørsett, and A. Zanna, Lie-group methods, Acta Numer., 9 (2000), pp. 215–365.
[13] A. Iserles and S. P. Nørsett, On the solution of linear differential equations in Lie groups, Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 357 (1999), pp. 983–1019. · Zbl 0958.65080
[14] W. Magnus, On the exponential solution of differential equations for a linear operator, Communications on pure and applied łdots, VII (1954), pp. 649–673. · Zbl 0056.34102
[15] C. Moler and C. Van Loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, SIAM Review, 45 (2003), pp. 3–49. · Zbl 1030.65029
[16] H. Munthe-Kaas and B. Owren, Computations in a free Lie algebra, Philos. Trans. A, 357 (1999), pp. 957–981. · Zbl 0956.65056
[17] J. Nievergelt, Parallel methods for integrating ordinary differential equations, Commun. ACM, 7 (1964), pp. 731–733. · Zbl 0134.32804
[18] M. Thalhammer, A fourth-order commutator-free exponential integrator for nonautonomous differential equations, SIAM J. Numer. Anal., 44 (2006), pp. 851–864. · Zbl 1115.65062
[19] M. Toda, Vibration of a chain with nonlinear interaction, J. Phys. Soc. Japan, 22 (1967), pp. 431–436.
[20] M. Valiev, E. Bylaska, N. Govind, K. Kowalski, T. Straatsma, D. W. H. J. J. van Dam, J. Nieplocha, E. Apra, T. Windus, and W. de Jong, NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations, Comput. Phys. Commun., 181 (2010), pp. 1477–1489. · Zbl 1216.81179
[21] A. Zanna, Numerical Solution of Isospectral Flows, Ph.D. thesis, University of Cambridge, 1998.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.