A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers. Application to quantum relativistic laser physics

Authors :: Antoine, X
Lorin, E
Institut Élie Cartan de Lorraine (IECL)
Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX)
Inria Nancy - Grand Est
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Centre de Recherches Mathématiques [Montréal] (CRM)
Université de Montréal (UdeM)
School of Mathematics and Statistics [Ottawa]
Carleton University
X. ANTOINE was partially supported by the French National Re-search Agency project NABUCO, grant ANR-17-CE40-0025.
E. LORIN received supportfrom NSERC through the Discovery Grant program.
ANR-17-CE40-0025,Nabuco,Frontières numériques et couplages(2017)
Publication Year :: 2018
Publisher :: HAL CCSD, 2018.
Abstract: A simple time-splitting pseudospectral method for the computation of the Dirac equation with Perfectly Matched Layers (PML) is proposed. Within this approach, basic and widely used FFT-based solvers can be adapted without much effort to compute Initial Boundary Value Problems (IBVP) for the time-dependent Dirac equation with absorbing boundary layers. Some numerical examples from laser-physics are proposed to illustrate the method.

Subjects :: Perfectly Matched Layers
high-order accuracy
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Dirac equation
pseudospectral approximation
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
time-splitting

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