Institute for Mathematical Modeling RAS
Dynamic load balancing.
Overview.
Simulation of combustion problems using multiprocessor computer systems
•
For the "chemical part" of the problem the computational costs are very expensive and each point depends
strongly on values of temperature and species concentration and can not be predetermined before
calculation. In our case the calculation of chemical reactions requires more than 90% of total computational
time. The reason of such fact is that in some of chemical processes the time of reactions is very small in
comparison to gas dynamic time.
•
Many of the species exist and react only in the quite narrow region
- in the flame front. The equal number of numerical points per
processor does not imply the load balancing automatically
therefore the special software was developed. The modified
"processor farm" principles with master controlled data exchange
between worker-nodes were used to achieve load balancing for
chemical kinetic part.
CH4 concentration
CO concentration
The combustion zone
65%
5%
30%
CH4
M.Iakobovski
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Institute for Mathematical Modeling RAS
M.Iakobovski
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Institute for Mathematical Modeling RAS
Dynamic load balancing.
Problem statement.
The system of equations, governing gas-dynamic and chemical kinetic processes under combustion,
expressed in operator form is the following:
U
 AU  f ,
t

U   ,  y ,  u,  v, E
( i)

T
f  (0, i ,0,0,0) T
Here A is a nonlinear operator,  - density,
y(i) - mass fraction of the i-th species,
u, v - components of velocity along x and y respectively,
p - pressure, E - total energy,
I - mass velocity of formation of substance in all responses.
I. Gasdynamic block (GD):
U
 AU  0
t
GD block is approximated via half-implicit finite-difference scheme
U j 1  U j 1
  A U j 1  A U j   0.
t
2
II. Block of chemical kinetics (CHEM):
dU
 f,
dt
M.Iakobovski
f  (0,  i , 0, 0, 0)T
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Institute for Mathematical Modeling RAS
Dynamic load balancing.
Goals.
sec
Calculation time using
domain decomposition
20.00
15.00
ideal time
10.00
5.00
29
27
25
23
the number of processor
21
19
17
15
11
13
9
5
0.00
7
t
i
m
e
25.00
1
Independent tasks are assigned to the
nodes of the mesh, which is distributed over
processors according to the domain
decomposition method
p
r
o
c
e
s
s
i
n
g
3
The main goal was to develop a library for
dynamic load balancing of loosely coupled
distributed tasks when using a
heterogeneous multiprocessor systems
Р1
When a task is processed, the result should
be returned to the corresponding processor
regardless where it was obtained
M.Iakobovski
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Institute for Mathematical Modeling RAS
Dynamic load balancing.
Issues.
Algorithm is based on collective farm, but is devoid of its
shortcoming. It is achieved due to a great reduction of traffic as
each processing node possesses equal controlling features.
Two (or more) processes are executed on each node communication (control) process and operating process
(or processes).
Algorithm for load balancing is based on the following principles:
• each processor primarily operates its local points (that are
stored in its memory);
• the processor can request points from the others provided that
a) all local points are calculated or transferred for handling to
other processors;
D
b) transmission of points for handling to other
processors and handling of local points
B
are fulfilled simultaneously.
A
Calculation process
Control process
Processor
D
D
task
B
A
A
E
C
M.Iakobovski
B
E
C
E
C
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Institute for Mathematical Modeling RAS
Dynamic load balancing.
Status.
•
•
•
Client
The dynamic load balancing
High speed network
library was developed. The
Mbyte/sec
library allows to efficiently
schedule the stream of tasks,
which are distributed according
to the domain decomposition
Server
Low speed network
method.
32 processors
12 processors
The library provides efficient use
of metacomputers. The mesh
speedup
may be stored within one or both
41.00
clusters
36.00
31.00
Cluster1
Cluster3
An approach is
CFD
Chemical
26.00
offered to the
integration of
21.00
Control
more than two
16.00
clusters for
11.00
Cluster2
Cluster4
solving
6.00
Chemical
Chemical
Np
combustion
1.00
problems
1 5 9 13 17 21 25 29 33 37 41 45
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