WIAS Preprint No. 2767, (2020)
Additive splitting methods for parallel solution of evolution problems
- Amiranashvili, Shalva
- Radziunas, Mindaugas
- Bandelow, Uwe
- Busch, Kurt
- Čiegis, Raimondas
2010 Mathematics Subject Classification
- 41A25 65N12 65Y20 65Y05 68Q25 68W10
- Splitting method, Richardson extrapolation, nonlinear Schrödinger equation, nonlinear optics
We demonstrate how a multiplicative splitting method of order P can be used to construct an additive splitting method of order P + 3. The weight coefficients of the additive method depend only on P, which must be an odd number. Specifically we discuss a fourth-order additive method, which is yielded by the Lie-Trotter splitting. We provide error estimates, stability analysis, and numerical examples with the special discussion of the parallelization properties and applications to nonlinear optics.
- J. Comput. Phys., 436 (2021), pp. 110320/1--110320/14, DOI 10.1016/j.jcp.2021.110320 .