Two-step perfectly matched layer for arbitrary-order pseudo-spectral analytical time-domain methods

Journal Article · Mon Oct 01 00:00:00 EDT 2018 · Computer Physics Communications

DOI:https://doi.org/10.1016/j.cpc.2018.09.015· OSTI ID:1543537

Shapoval, Olga ^[1]; Vay, Jean-Luc ^[1]; Vincenti, Henri ^[2]

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1. Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
2. University Paris-Saclay, Gif-sur-Yvette (France)

Numerical simulation of an electrodynamic system in empty space requires the implementation of open boundary conditions (BC) to terminate the solution of Maxwell’s equations on the boundaries of the computational domain. The Perfectly Matched Layer (PML) has become the method of choice for open BC with wave equations, as it is straightforward and relatively easy to implement, and offers very efficient and user-adjustable absorption rates. PMLs are most often employed with the Finite-Difference Time-Domain (FDTD) algorithm, which in its most common implementation offers second-order accuracy in space and time on Cartesian grids. Yet, simulations (including some class of electromagnetic Particle-In-Cell simulations) that require higher precision may resort to higher-order Maxwell solvers employing extended finite-difference stencils, or even to pseudo-spectral Maxwell solvers, for which a general, versatile and efficient formulation of the PML has been missing so far. Here we propose a novel “two-step” formulation of the PML that is simple, very versatile and can be used as is with any Maxwell solver. In particular, it is applicable to a large class of Maxwell solvers including the arbitrary-order Pseudo-Spectral Analytical Time-Domain (PSATD) solver, which offers arbitrarily low numerical dispersion when increasing solver order and becomes dispersion-free at infinite order. Analysis and numerical simulations demonstrate that the new formulation is as efficient as the standard PML formulation, both for the FDTD and the PSATD implementations.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-05CH11231; AC02-06CH11357
• OSTI ID: 1543537
• Journal Information: Computer Physics Communications, Journal Name: Computer Physics Communications Journal Issue: C Vol. 235; ISSN 0010-4655
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
APML
FDTD
Maxwell’s equations
PML
PSATD
PSTD
asymmetric perfectly matched layer
finite-difference time-domain method
perfectly matched layer
pseudo-spectral analytical time domain method
pseudo-spectral time domain method