**Abstract** : The execution of scientific applications on parallel
architectures often dictates an efficient decomposi-
tion of the computational load in order to ensure
high performance. In literature, such applications
often use graph theory to describe and solve the
problem of distributing computations to a number
of available processors .
More precisely each vertex of a graph rep-
resents a computation (related to a mesh ele-
ment), while an edge represents data dependen-
cies between computations. Under this context,
to equally distribute the computations of a paral-
lel application, one may perform a graph partition-
ing in k parts and assign each resulting part to a
processor of the parallel machine. In other words,
the objective of graph partitioning is to divide the
given graph into k smaller parts of roughly equal
size such that the number of edges between differ-
ent parts is minimised. Unfortunately, graph partitioning is known to
be NP-hard [2], so finding a partition of a given
graph is usually based on heuristic techniques.
Nowadays, the most common approaches to solve
the graph partitioning problem are based on the
multilevel approach to compress the problem
and on the recursive-bisection heuristic to solve it
on a smaller instance. Mature software for graph
partitioning exist, such as Metis or Scotch.
Recent challenges emerging in scientific com-
puting involve the deep understanding of more
complex physical phenomena. In an attempt to
efficiently address the above issue, modern simu-
lations have been developed that combine differ-
ent component models, plugged in together under
a coupling environment (coupled simulations).
Examples of coupled simulations follow the
multi-physics or multi-scale paradigm. For in-
stance to simulate real-word conditions under the
multi-physics model, one must consider the impact
of a number of different physics that occur con-
currently and correspond to different component
simulations. In this context, modeling approaches
should take into consideration the existence of dif-
ferent computational domains but also their poten-
tial overlapping invoked due to data dependencies
between different components.
Nowadays, to solve the load balancing problem
of coupled simulations, one simply treats each
component as a completely independent simulation
and thus a classic graph partitioning algorithms is
applied to each of the N components separately. As
far as we know, the above approach to partition
coupled simulations, which we call naive approach,
is the most commonly used method and little work
has been done to address the problem in a more
sophisticated way.
While naive approach is evidently easy to use
and solves the partitioning problem for each com-
ponent separately, it fails to address the real chal-
lenges of coupled simulations, that is, balancing the
load during the overlapping of computational do-
mains and minimise the additional communication
costs between parts that belong to different com-
ponents.More precisely even though the partition
of each component corresponds to a balanced dis-
tribution of the load on its entire computational
domain, if we focus just on the overlapping inter-
face, we observe that the load is not necessarily
balanced.
In this work, we propose graph partitioning
techniques that address the problem of load bal-
ancing for coupled simulation, which we refer to as
co-partitioning. The main idea here is to perform a
“coupling-aware” partitioning, instead of partition-
ing each component independently.
Here, we present an experimental study on real-
life coupled simulations. More precisely, we test
our algorithms on applications coming from the
field of aeronautic propulsion where the behavior
of hot components is impacted by complex interac-
tions between different physics. To predict such
thermal environments, coupling of different heat
transfer models, such as turbulent combustion, ra-
diation and heat conduction, is necessary. Note
that previous tests on synthetically generated cases
aspire promising results for the graph partitioning
of coupled applications when the proposed algo-
rithms are used. New results on the real-life test
cases are presented and evaluated in this work.