Time-Dependent B-Spline R-Matrix Method without Explicit R-Matrix Calculation

Combining the time-dependent R-matrix (TDRM) method [Phys. Rev. A 79, 053411 (2009); New J. Phys. 11, 093014 (2009)] and B-spline, we develop a parallelizable numerical method to solve the time-dependent Schrodinger equation following the spirit of R-matrix theory. In the TDRM method, a linear solver approach is applied at each time step in order to obtain the R-matrix, which is needed for the propagation relation for the wave function. However, in our method, by using the feature of the B-spline at the boundary of a subregion, we can obtain the relation without an explicit calculation of the R-matrix. For that, we only need to solve a linear matrix equation Ax = b, where b is a matrix composed of only three column vectors. Thus, the amount of calculation is highly reduced, so the computing speed is improved over that for the TDRM. By applying the method to above threshold ionization (ATI) of a one-dimensional model, we confirmed that our numerical method operates well.