Journal of Software Engineering and Applications, 2011, 4, 546-549
doi:10.4236/jsea.2011.49063 Published Online September 2011 (
Copyright © 2011 SciRes. JSEA
Multi-Domain Parallel Computing for Strength
Analysis of Whole Aircraft Model
Xiuhua Chen, Hai Wang, Yubo Ding
School of Aeronautics and Astronautics, Shanghai JiaoTong University, Shanghai, China.
Received July 25th, 2011; revised August 20th, 2011; accepted August 28th, 2011.
In the Windows XP 64 bit operating system environment, several common PC were used to build a cluster system, es-
tablishing the distributed memory parallel (DMP) computing system. A finite element model of whole aircraft with
about 260 million degrees of freedom (DOF) was developed using three-node and four-node thin shell element and
two-node beam element. With the large commercial finite element software MSC.MARC and employing two kinds of
domain decomposition method (DDM) respectively, realized the parallel solving for the static strength analysis of the
whole aircraft model, which offered a high cost-effective solution for solving large-scale and complex finite element
Keywords: Parallel Computing, Whole Aircraft Model, Static Strengt h , Do m ain Decompo sit ion
1. Introduction
With the steady development of domestic aviation indus-
try, especially the further research of commercial aircraft
engineering, all kinds of large-scale and complex struc-
tures are encountered. These structures are not only with
huge dimensions but also with more complicated condi-
tions, even related to kinds of geometrical, material,
contact nonlinearity problems. For these problems, tradi-
tional finite element methods (FEM) running on single
PC can’t satisfy the need of engineering practice. The
technology of parallel computing is introduced into finite
element analysis to increase the scale of structure analy-
sis, accelerate computing speed, and facilitate the appli-
cation of finite element in large-scale and complex
Parallel systems and multi-core systems are quite com-
mon these days. While most solvers focus on paralleliz-
ing only one aspect of solution (namely, matrix solution),
MSC.MARC parallelizes all the steps of analysis (as-
sembly, matrix solution and stress recovery). This en-
ables researchers to get more out of the hardware.
Parallel finite element method (FEM) based on domain
decomposition method (DDM) is one of the most active
research orientations in current parallel computing field.
At present, in rock-soil mechanics [1,2], computational
fluid dynamics (CFD) [3] and other domains, domestic
scholars have carried out extensive research. However,
there is scarce engineering practice for strength analysis
of large-scale aero structure mainly composed of plate,
shell and beam. One reason is that studying to domain
decomposition method (DDM) are not enough to make
research deep into and few of methods can effectively
implement the domain decomposition of large-scale and
complex structures. The other is that most of researchers
focus on the study of theories and few software available
can be applied to practice. This paper practice the spe-
cific application in the strength analysis of whole aircraft
model with millions node degree of freedom and intro-
duce the optimal decomposition method.
2. Establishing of PC Cluster
The study in this paper is based on PC cluster and its
architecture is shown in Figure 1.The PC cluster is com-
posed of one host node and several slave nodes. Both
host and slave nodes are used to participate in computing.
The PC cluster, with the ability of distributed memory
and storage, greatly enhance the performance of the
whole system.
According to the scale and complexity of the whole
aircraft finite element model, one host node and eight
slave nodes were used to build the PC cluster. Each node
has the same configuration as shown in Table 1.
Multi-Domain Parallel Computing for Strength Analysis of Whole Aircraft Model 547
Table 1. Specification of software and hardware.
Parameter Specification
Number of Processor 9
Type of Processor Intel Core2 dual-core E7400
Basic Frequency 2.8 GHZ
Memory Capacity 4 G
Disk Capacity 160 G
Executive Routine MSC.Marc 2005r2
Operating System Windows XP 64 bit
Communication Environment MP-MPICH 1.2
Network Environment 10 ~ 100 Mbps Ethernet
3. Parallel Finite Element Comp uting
3.1. Whole Aircraft Finite Element Model
According to the actual structure of aircraft, the whole
aircraft finite element model, as shown as Figure 2, was
developed. It contained 463532 elements (including
418220 three-node and four-node thin-shell elements and
45312 two-node beam elements) and 437501 nodes
(about 2.6 million DOF).The load and boundary condi-
tions were defined as following: four clamped supports
were applied to lower fuselage sections; uniform distri-
bution of load was applied to the wingtips of wing and
horizontal tail respectively; a certain amount of concen-
trated load was applied to upper fuselage sections. Be-
cause the scale of the whole aircraft finite element model
is greatly beyond the solving ability of one PC, parallel
finite element method (FEM) based on domain decom-
position method (DDM) was adopted to solve the prob-
3.2. Parallel Finite Element Based on DDM
Parallel finite element method (FEM) based on domain
decomposition method (DDM) is a coarse-grain parallel
Figure 1. Architecture of PC cluster.
method [4]. Its basic thought is “divide and rule”, that is,
decomposing the entire domain into several subdomains,
then mapping each subdomain to corresponding proces-
sor and each processor simultaneously dealing with its
corresponding subdomain. At last, collect the results and
get the final solution. The flow chart is shown as Figure
3 [4].
3.3. Domain Decomposition Implement
Two kinds of domain decomposition method, vector and
radial decomposition, were employed respectively. Vec-
tor decomposition refers to decomposing along a certain
vector direction and radial composition along the radial
direction of a certain circle. The schematic diagrams are
shown as Figure 4(a) and (b).
According to the two methods above, the whole air-
craft finite element model was decomposed into nine
subdomains. The meshes before and after decomposition
were shown as Figures 5-7.
Figure 2. Finite element model of the whole aircraft.
Copyright © 2011 SciRes. JSEA
Multi-Domain Parallel Computing for Strength Analysis of Whole Aircraft Model
Collection of Results
FE Model
FE Parallel
Output of Results
Figure 3. Flow chart of parallel finite element method.
(a) (b)
Figure 4. Schematic diagram. (a) Vector decomposition; (b)
Radial decomposition.
Figure 5. Meshes before decomposition.
Figure 6. Meshes after vector decomposition.
Statistics the scales of subdomains, then list them in
Table 2. In the table, subdomain 1 ~ 9 refers to subdo-
mains after decomposition respectively; total is equal to
algebraic sum of the scale of each subdomain; entire do-
main means finite element model of the whole aircraft;
the degrees of freedom of each domain are calculated by
six times of the number of nodes, that is, of them includ-
ing the constraint degrees of freedom. Generally Speak-
Figure 7. Meshes after radial decomposition.
ing, two factors can influence on the quality of decom-
posed domain [5]. One is that each subdomain almost
possesses the same degrees of freedom, that is, so-called
load balance. The other is that the number of inter-do-
main nodes is as fewer as possible. From Table 2, it can
be seen as follows:
For the two methods, degree of freedom of each sub-
domain is not equal.
In contrast, radial decomposition is better than vector
decomposition in load balance, while vector decom-
position gets fewer of nodes of inter-domains, that is,
fewer of degrees of freedom.
3.4. Results and Analysis
After FE parallel solving, got the misses stress distribu-
tion of the model as shown in Figure 8.
Statistics the wall time and CPU time of each subdo-
main as shown in Table 3 . In the table, node 1 ~ 9 com-
Table 2. Scales of different domainsa.
Vector Decomposition Radial Decomposition
Num-ENum-NDOF Num-E Num-NDOF
SD 1 51504 50183 301098 60542 56696 340176
SD 2 51504 49514 297084 72519 69562 417372
SD 3 51504 49599 297594 41658 41076 246456
SD 4 51504 49861 299166 44720 45568 273408
SD 5 85998 81811 490866 52343 53140 318840
SD 6 19189 18802 112812 55603 53996 323976
SD 7 49323 47611 285666 35603 34417 206502
SD 8 66434 60596 363576 50273 47487 284922
SD 9 36572 34355 206130 50271 47485 284910
Total 463532442332 2653992 463532 449427 2696562
EnD 463532437501 2625006 463532 437501 2625006
InD ――― 4831 28986 ――― 1192671556
a abbreviations in this table: Sub-Domain(SD), Entire Domain(EnD), Inter
Domain(InD), Number of Element(Num-E), Number of Node(Num-N),
Degree of Freedom(DOF).
Copyright © 2011 SciRes. JSEA
Multi-Domain Parallel Computing for Strength Analysis of Whole Aircraft Model 549
Figure 8. Mises stress distribution in the whole FEM.
Table 3. Computing time of nodes.
Vector Decomposition Radial Decomposition
Wall Time (s) CPU Time (s) Wall Time (s) CPU Time (s)
Node 1 1799.44 840.30 2108.23 1090.50
Node 2 1799.42 567.80 2108.24 662.44
Node 3 1799.34 541.11 2108.11 236.38
Node 4 1799.28 466.86 2108.05 412.12
Node 5 1799.20 824.36 2107.97 485.83
Node 6 1799.14 114.09 2107.92 478.77
Node 7 1799.08 567.73 2107.86 233.42
Node 8 1799.03 633.33 2107.81 642.27
Node 9 1798.97 243.59 2107.74 660.55
Time 1846.27 842.09 2154.01 1092.19
puted the corresponding subdomain 1 ~ 9 respectively
and total time is the elapsed time to compute the whole
model, including total wall time and CPU time. It can be
seen from Table 3 that for each computing node, wall
time is nearly equal, but the CPU time not. That is de-
termined by the load distribution on each computing
node and the number of inter-domain nodes. Also, it can
be seen from the item of total time that vector decompo-
sition has a little advantage, that is, although vector de-
composition is not better than radial decomposition in
load distribution, the less number of inter-subdomain
nodes greatly decrease the total time. Of course, for a
model with large scale and high complexity, it is not at
ease to achieve both load balance and least communica-
tion overhead. In short, taking over half an hour to solve
such model successfully on the common PC cluster, no
doubt, is high cost-effective.
4. Conclusions
PC cluster based on Windows XP 64-bit system is an
ideal, high cost-effective parallel system with the ability
of distributed memory and storage and able to achieve
the parallel solving of large-scale finite element model.
Domain decomposition method (DDM) is coarse-grain
parallel strategy and fit for PC cluster system. In the sys-
tem, each computing node is just in charge of corre-
sponding subdomain and only exchanges the information
and data in the public area among subdomains.
Both vector and radial decomposition is able to decom-
pose complex finite element meshes, which is of great
significance for the large-scale aero structure mainly com-
posed of plate, shell and beam.
The choice of domain decomposition method is very
important. In order to achieve higher efficiency, two as-
pects should meet. One is load balance, and the other is
minimizing the number of inter-domain nodes. The com-
putational efficiency of parallel finite element method
(FEM) based on domain decomposition method (DDM)
is determined by the balance of the two aspects above.
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