A perfectly matched layer applied to a reactive scattering problem

Abstract

The perfectly matched layer (PML) technique is applied to a reactive scattering problem for accurate domain truncation. A two-dimensional model for dissociative adsorbtion and associative desorption of H(2) from a flat surface is considered, using a finite difference spatial discretization and the Arnoldi method for time-propagation. We compare the performance of the PML to that of a monomial complex absorbing potential, a transmission-free complex absorbing potential, and to exterior complex scaling. In particular, the reflection properties due to the numerical treatment are investigated. We conclude that the PML is accurate and efficient, especially if high accuracy is of significance. Moreover, we demonstrate that the errors from the PML can be controlled at a desired accuracy, enabling efficient numerical simulations.

Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

“…The PML scheme for the TDSE is usually derived by assuming that the potential is both spatially and temporally invariant, and then modal analysis is performed on the Laplace-transformed equation to ensure that the solution decays outside the interior domain, i.e., jxj >R 0 . [34][35][36] The transformation can be formulated as…”

“…The PML scheme for the TDSE is usually derived by assuming that the potential is both spatially and temporally invariant, and then modal analysis is performed on the Laplace‐transformed equation to ensure that the solution decays outside the interior domain, i.e., R 0 . The transformation can be formulated aswhere is a constant referred to as the absorption strength, and f is the absorption function.…”

“…Zheng used it to solve the nonlinear Schrödinger equation, [34] and Nissen and Kreiss have since tried to optimize the PML method for the Schrödinger equation with time-independent potentials [35] and have, together with Karlsson, applied it to a reactive scattering problem. [36] PMLs have also been applied to time-dependent density functional theory (TDDFT) [37] and the Dirac equation. [38] It is, however, surprising how comparatively little work has been done on applying PMLs in Schrödinger problems, in particular, for explicitly timedependent problems, such as intense laser-matter interactions.…”

Wave packet simulations of antiproton scattering on molecular hydrogen

“…1 numerically with a Chebyshev time propagation scheme 17 . A perfectly matched layer (PML) 18 at the edges of the numerical grid has been used absorb the wavefunction and to avoid spurious reflections.…”

Multiconfigurational time-dependent Hartree method to describe particle loss due to absorbing boundary conditions

“…Other absorbing operators are also common, such as the so-called transformative CAP (TCAP) [18], which is more or less equivalent with the non-local CAP obtained using smooth exterior scaling [19] or perfectly matched layers [20]. While exact and space-local absorbing boundary conditions may be formulated [21], they are in general non-local in time, and therefore impractical.…”