Asymmetric PML for the absorption of waves. Application to mesh refinement in electromagnetic particle-in-cell plasma simulations Page: 2 of 10
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Taking advantage of the high rates of absorption of the APML, we have de-
vised a new strategy for introducing the technique of Mesh Refinement into
electromagnetic Particle-In-Cell plasma simulations. Previous attempts have
relied on algorithms of various complexity to connect calculations of EM fields
at the border of regular grids at different resolutions (we will refer these as
"sewing" algorithms). Most were unstable at small wavelengths while the sta-
ble ones suffered form inherent limitations on their ability to avoid spurious
wave reflection at interfaces and were complicated to implement (6). Instead,
we propose a technique by substitution. We present the details of the algo-
rithm as well as a 2-D example of its application to laser-plasma interaction
in the context of fast ignition.
2 Definition of the APML
This section summarized results presented in (5), in which the reader can find
a complete presentation of the APML.
For the transverse electric (TE) case, we define the APML as
OEF cyO (1)
o +oyE=- + yHz ()
at c By
o _ + Ec + (2)
Ht c Ox
OHzx a*Hzx = ZOE E (3)
o t c Ox
o H + a*Hzy = OE +* E (4)
0t c y y
Hz = Hz+ Hzy (5)
For cx = cy = c* = c* = c and -a = ?T =(T* = Qy = 0, this system
reduces to the Berenger PML medium, while adding the additional constraint
ax = ay = a* = a* = 0 leads to the system of Maxwell equations in vacuum.
It can be shown (5) that if c = c*, cy = c*, Th = *, Qy = ,*, Q = and
= then the impedance of an APML medium is Z = + po/o, which
is the impedance of vacuum. Hence, like the PML, given some restrictions
on the parameters, the APML does not generate any reflection at any angle
and any frequency. Just as for the PML, this property is not retained after
discretization (5).
We assume that we have an APML layer of thickness 6 (measured along x)2
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Vay, J. L.; Adam, J. C. & Heron, A. Asymmetric PML for the absorption of waves. Application to mesh refinement in electromagnetic particle-in-cell plasma simulations, article, September 24, 2003; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc736429/m1/2/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.