NEW DATA COMPRESSION FOR MULTI-DIMENSIONAL
NUMERICAL SIMULATION
MITSUE DEN
Hiraiso Solar Terrestrial Research Center, CRL
3601 Isozaki, Hitachinaka, Ibaraki 311-1202, Japan
AND
KAZUYUKI YAMASHITA AND RYOJI MATSUMOTO
Chiba University,
1-33 Yayoi, Inage, Chiba 263-8522, Japan
With an increase in the processing speed, we can perform multi-dimensional numerical simulations. On the other hand, we are facing with problems that we have to handle huge amount of output data. We can attain
higher time resolution in the analysis of simulation results by storing evolutional sequence more frequently. However, that interval is limited by the
disk space and the speed of I/O. To overcome this dilemma, we propose a
new real time data compression algorithm.
Our compression algorithm is as follows. (1) Set contour levels (say,
28 = 256 levels) to cover the dynamic range of the original data. (2) Classify the original data according to the specied contour levels. (3) Make
a conversion table which relates the original data and the contour levels.
The values of oating point variables at each mesh point are quantized
to specied contour levels. Information is partly lost here and then the
data are compressed. When the compression eciency (CE) is dened by
CE = 10m=r, where r and m are the size of the original and the compressed
data respectively, we can always attain CE = 75% at the this step if the
original data are stored in single precision variables. Since the quantized
data are still sequential text stream, we can compress them furthermore
by using lossless compression tool, i.e., the data go through compression
two times in our method. For real time lossless compression during the
simulation, we adopt the LZW15V.C.
In order to investigate eciency of our algorithm, we calculate CE for
three models, (I) supernova explosion as a model for the single density
peak and the logarithmic density distribution, (II) formation of the large
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MITSUE DEN ET AL.
scale structure as a model for the multiple density peaks and the linear
density distribution, and (III) emergence of twisted magnetic ux tubes
for the test of vector variables such as magnetic elds. Three-dimensional
numerical simulation have been carried out for each model and more than
90% eciency is achieved for all models (see Table 1).
It should be noted that our compression algorithm is `lossy', which
means that the original data cannot be restored perfectly from the compressed data. However, our compression method is useful for visualization
and analysis of numerical results. Thus we conclude that it is apposite to
huge amount of data such as the results of 3D simulations.
TABLE 1. File sizes and compression eciencies for
models I, II and III. R, M and C2 mean the raw data,
quantized (or mapped) data and the second time compressed data, respectively.
Model
R (byte)
M (byte)
C2 (byte)
CE (%)
I
1372008
343008
97488
92.9
II
4000008
1000008
77016
98.1
III-Bx
842732
210689
76078
91.0
III-By
842732
210689
72426
91.4
III-Bz
842732
210689
73656
91.3
Figure 1.
Comparison of the original data (left) and the compressed data (right) for
model III (emergence of the magnetic ux tubes). The white surface indicates the isosurface of magnetic eld strength, the gray curves show the magnetic eld lines and the
gradated monotone walls in the simulation box show the density distribution.