2000 PROGRESS REPORT - ENEA - Fusione

1. Magnetic Confinement
s u
16
12
8
4
0
N ppc = 4
N ppc = 16
N ppc = 64
N ppc = 256
2 4 6 8
n proc
Fig. 1.45 - Speed-up vs the number Fig. 1.45 of processors, at fixed number
of (8-processors) nodes, n node =2, for the domain decomposition
version, ν2a
ν2a
inter-node particle decomposition and the
intra-node domain decomposition, which
do not require the introduction of the grid
auxiliary array introduced in version ν1,
but implies heavier restructuring of the
code and, possibly, addressing loadbalancing
problems. It consists of reordering
the particle population according
to the portion of domain in which each
particle resides, and assigning a different
portion to each processor. Such a
reordering gives rise, once again, to the
risk of race conditions (the particles
belonging to a certain domain portion
have to be counted within a particle loop,
and the updating of the counter is a
critical operation). Once assigned to the
processors, however, no further race
condition occurs in updating the pressure
array element, as loop iterations, which
could, in principle, concur to the updating
of the same element, are executed by the
same processor. Figure 1.45 shows the
scaling of the speed-up as compared to
n proc , at the fixed number (n node =2) of
8-processors nodes, obtained by this
version. The speed-up values, obtained
with the version ν2a, do not seem to be
very satisfactory. In fact, several operations, which are absent in the intra-node particle
decomposition version ν1, will have to be performed anyway: namely, the identification of the
domain portion into which each particle falls, a loop to balance the particles over processors, and
a re-ordering loop. However, for specific (but rather common) applications characterized by a
contained particle migration per time step from one portion of the domain to the other, a
significant efficiency improvement can be obtained by limiting the reordering phase (and then,
the critical computation) to those particles that have changed their domain portion in the last
step. Their number can be very low indeed, if it is possible to decompose the domain along a
slowly-varying coordinate. Figure 1.46 shows a comparison between the results obtained by the
version ν2a and a companion version (ν2b), which implements such a selective reordering. The
results of the particle decomposition implementation, ν1, are also shown for reference. The case
N ppc =256 is considered as an example.
It can be concluded that, at least for the specific application considered here, this mixed
“particle-domain decomposition” strategy represents an interesting compromise between the two
competing targets — namely, high speed-up and low memory requirements.
1.4.5 Non-linear zonal dynamics of drift and drift-Alfvén turbulences in
tokamak plasmas (In collaboration with University of California at Irvine
and Princeton University Plasma Physics Laboratory)
In recent years, increasing attention has been devoted to exploring non-linear dynamics of zonal
flow [1.27] associated with electrostatic drift-type turbulence [1.28-1.30]. On the other hand,
though it is well known how electrostatic drift modes couple to the electromagnetic shear Alfvén
wave as the plasma β=8πP/B2 increases [1.31-1.33], little effort has been devoted so far to
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