Nonstandard finite difference schemes for the two-level Bloch model
Splitting methods with very large CFL
Abstract
In this paper, we present splitting schemes for the two-level Bloch model. After proposing two ways to split the Bloch equation, we show that it is possible in each case to generate exact numerical solutions of the obtained sub-equations. These exact solutions involve matrix exponentials which can be expensive to compute. Here, for $2\times2$ matrices we develop equivalent formulations which reduce the computational cost. These splitting schemes are nonstandard ones and conserve all the physical properties (Hermicity, positiveness and trace) of Bloch equations. In addition, they are explicit, making effective their implementation when coupled with the Maxwell equations.
Type
Publication
International Journal of Modeling, Simulation, and Scientific Computing, 9(4), 1850033:1–23 (2018)
