SciDAC-II Compass The Heavy Ion Fusion Science Virtual National Laboratory 1 Vay - APS-DPP 2011 Novel Simulation Methods in the Particle-In-Cell Framework Warp J.-L. Vay*, C.G.R. Geddes Lawrence Berkeley National Laboratory, CA, USA D.P. Grote, A. Friedman Lawrence Livermore National Laboratory, CA, USA 53 rd Annual Meeting of the APS Division of Plasma Physics Salt Lake City, Utah, USA – November 14-18, 2011 SciDAC-II Compass The Heavy Ion Fusion Science Virtual National Laboratory *jlvay@lbl. gov
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SciDAC-II Compass SciDAC-II Compass The Heavy Ion Fusion Science Virtual National Laboratory 1 Vay - APS-DPP 2011 Novel Simulation Methods in the Particle-In-Cell.
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SciDAC-IICompass
The Heavy Ion Fusion Science Virtual National Laboratory 1Vay - APS-DPP 2011
Novel Simulation Methods in the Particle-In-Cell Framework Warp
J.-L. Vay*, C.G.R. GeddesLawrence Berkeley National Laboratory, CA, USA
D.P. Grote, A. FriedmanLawrence Livermore National Laboratory, CA, USA
53rd Annual Meeting of the APS Division of Plasma PhysicsSalt Lake City, Utah, USA – November 14-18, 2011
SciDAC-IICompass
The Heavy Ion Fusion Science Virtual National Laboratory*[email protected]
SciDAC-IICompass
The Heavy Ion Fusion Science Virtual National Laboratory
Markers
2Vay - APS-DPP 2011
Warp is a versatile parallel 3D Particle-In-Cell framework developed by the Heavy Ion Fusion Science Virtual National Laboratory
Predicted speedup: >10,000 for 10 GeV stage; > 1,000,000 for 1 TeV stage.
Boosted frame g = gwakeLab frameCalculation in boosted frame at ≈wake minimizes scale differences1
SciDAC-IICompass
The Heavy Ion Fusion Science Virtual National Laboratory
An electromagnetic solver based on Non-Standard Finite-Difference (NSFD) was implemented in Warp
NSFD: weighted average of quantities transverse to FD ().
NSFD=FD if =0
Yee Cole-Karkkainen (CK)
Yee/CK allows for perfect dispersion along 3D/principal axes.
x=y=z)
Cole1 and Karkkainen2 have applied NSFD to source free Maxwell equations
Warp3: switched FD/NSFD to B/E.
=> FD on source terms, i.e. standard exact current deposition schemes still valid.
*
FD
NSFD
a
b
bb
b
g
g
g
g-a
-b
-b -
b
-b
-g
-g
-g
-g
Dx
NSFD
FD
FD
NSFD
3J.-L. Vay, et al., J. Comput. Phys. 230 (2011) 5908.
x=y=z)
Vay - APS-DPP 2011 4
1J. B. Cole, IEEE Trans. Microw. Theory Tech. 45 (1997), J. B. Cole, IEEE Trans. Antennas Prop. 50 (2002).2M. Karkkainen et al., Proc. ICAP, Chamonix, France (2006).
NSFD offers tunability of numerical dispersion
perfect dispersion 2D diagonal isotropic
SciDAC-IICompass
The Heavy Ion Fusion Science Virtual National Laboratory
Example: Reflection of circular pulse
using 5 cells PML
with quadratic progression
and standard coefficients
or improved coefficients2
5
Perfectly Matched Layer1,2 (PML) implemented with NSFD solver - for absorption of outgoing waves -
Same high efficiency as with Yee.1JP Berenger, J. Comput. Phys. 127 (1996) 3632J.-L. Vay, J. Comput. Phys. 183 (2002) 367
NSFDNSFD
FDFD
Vay - APS-DPP 2011
SciDAC-IICompass
The Heavy Ion Fusion Science Virtual National Laboratory
After testing: instability mostly insensitive to numerical dispersion… …but very sensitive to time step!
6Vay - APS-DPP 2011
Sharp decrease of instability level at ct=z/√2
Tunable NSFD solver allows ct=z/√2 time step for (near) cubic cells• ct=z/√2 time step restricted to “pancake” cells in 3D using Yee FDTD solver
Use of special time step was helpful but not sufficient for large g boost
Pow
er s
pect
rum
(a.
u.)
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The Heavy Ion Fusion Science Virtual National Laboratory 7Vay - APS-DPP 2011
Digital filtering of current density and/or fields -- commonly used for improving stability and accuracy
Multiple pass of bilinear filter + compensation routinely used
100% absorption at Nyquist freq.Bilinear (B)Bilinear (B) + compensation (C)
1/2 1/41/4
Bilinearfilter
Wideband filtering difficult in parallel (footprint limited by size of local domains) or expensive
Example: wideband filters using N repetitions of bilinear filter
1×B + C
4×B + C
20×B + C
50×B + C
80×B + C
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The Heavy Ion Fusion Science Virtual National Laboratory 8
“Strided” bilinear filters enable efficient and versatile filtering1