Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31473
Affine Combination of Splitting Type Integrators, Implemented with Parallel Computing Methods

Authors: Adrian Alvarez, Diego Rial


In this work we present a family of new convergent type methods splitting high order no negative steps feature that allows your application to irreversible problems. Performing affine combinations consist of results obtained with Trotter Lie integrators of different steps. Some examples where applied symplectic compared with methods, in particular a pair of differential equations semilinear. The number of basic integrations required is comparable with integrators symplectic, but this technique allows the ability to do the math in parallel thus reducing the times of which exemplify exhibiting some implementations with simple schemes for its modularity and scalability process.

Keywords: Lie Trotter integrators, Irreversible Problems, Splitting Methods without negative steps, MPI, HPC.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 750


[1] H.F. TROTTER, On the product of semigroups of operators. Proc. Amer. Math. Soc. 10( 1959), 545-551
[2] Strang G., 1963: Accurate partial difference methods II: Non Linear Problems.Numerische Math. 6 (1964) 37-46.
[3] B. Bidegaray C. Besse and S. Descombes, Order estimates in the time of splitting methods for the nonlinear Schringer equation, SIAM J. Numer. Anal 40 (2002).
[4] S. Pacheco, Parallel programming with MPI, (1997) by Morgan Kaufmann Publishers, Inc. San Francisco, California.
[5] Goldman, D. and Kaper T. J 1996, SIAM J. Numer. Anal., 33, 349.
[6] H. Yoshida, Construction of higher order symplectic integrators, Phys. Lett. A 150 (1990), 262?268.
[7] F. Neri, Lie algebras and canonical integration, Department of Physics report, University of Maryland (1987).
[8] R. D. Ruth, A canonical integration technique, IEEE Transactions on Nuclear Science NS 30 (1983), no. 4, 2669-2671.
[9] Leo, C.S.F. de la Vega, D. Rial, High order methods for irreversible equations, enviado a SIAM J. Numer. Anal.