=Paper=
{{Paper
|id=Vol-2267/410-414-paper-78
|storemode=property
|title=Accelerating real-time ship motion simulations using general purpose GPU computations
|pdfUrl=https://ceur-ws.org/Vol-2267/410-414-paper-78.pdf
|volume=Vol-2267
|authors=Ivan Petriakov,Ivan Gankevich,Vladimir Korkhov,Degtyarev Alexander
}}
==Accelerating real-time ship motion simulations using general purpose GPU computations==
https://ceur-ws.org/Vol-2267/410-414-paper-78.pdf
Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
ACCELERATING REAL-TIME SHIP MOTION
SIMULATIONS USING GENERAL PURPOSE GPU
COMPUTATIONS
Ivan Petriakov a, Ivan Gankevich b, Vladimir Korkhov c,
Degtyarev Alexander d
Saint Petersburg State University
E-mail: a st049350@student.spbu.ru, b i.gankevich@spbu.ru,
c
v.korkhov@spbu.ru, d a.degtyarev@spbu.ru
Software suites for ship simulations are typically used for statistical studies of ship dynamics, but also
as a simulator for training ship crew in dangerous situations. One problem that arises during training is
speeding-up a part of the session which does not involve actions from the crew. The aim of the study
reported here is to accelerate solution of ship motion equations using general purpose computations on
GPU. These equations describe dynamics of ship manoeuvring in wavy sea surface, and are central to
the simulator programme. The equations are solved numerically via Runge—Kutta—Fehlberg method.
Due to high number of floating point operations, computation on GPU achieves considerable speed-up
over CPU. High performance solution allows to shorten training sessions and make them more
efficient, but also beneficial for statistical studies as it reduces simulation time.
Keywords: GPGPU, OpenCL, ship dynamics, ocean waves, maritime simulator, virtual testbed
© 2018 Ivan Petriakov, Ivan Gankevich, Vladimir Korkhov, Degtyarev Alexander
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
1. Introduction
This work is carried out within framework of the Virtual testbed project which aims to create a
decision support system for simulating, predicting and preventing dangerous situations caused by
physical phenomena that may occur with the ship in sea way. The situations include: the flooding of
the compartment, the fire in the compartment, the loss of ship stability, large ocean waves and many
others. The main feature of the project is the usage of general purpose GPU computations to improve
performance. Other key feature is realistic marine objects. These are provided by IGES format, which
is vendor-neutral standard for exchanging object models between CAD systems. Finally, novel wavy
surface model used to simulate ocean waves [7], but at this stage it is not included in the project yet.
On-the-shore decision support system receives data in real-time from ships in the sea,
simulates ship motions; to be enable to make decisions the system have to simulate ship motions in
real-time. The technology that provides real-time performance is general purpose computations on
GPUs. Most of the computations in the programme involve large number of transcendental
mathematical functions, linear access to dense arrays and matrices, and no complex information
dependencies between computation stages. It allows us to use OpenCL framework as acceleration tool.
Simply rewriting source code in OpenCL is often not enough. We need to adapt algorithms
and transform mathematical formulae to make them efficient for GPU. The new mathematical
formulae for velocity potential computation was derived specifically for this use case. It uses fast
Fourier transforms to achieve high performance on GPU and is numerically equivalent to the known
formula from linear wave theory. Multidimensional derivatives is another algorithm which requires
completely different OpenCL implementation. We plan to write code generator that produces
optimised OpenCL programme for each particular derivative dimension and array shape. Finally,
geometric transformations (rotation and translation) are easy to do in OpenCL with lots of built-in
vector functions.
2. Related work
The feature that distinguishes the Virtual testbed from other similar projects is that it is not
only a ship motion simulator, but also a decision support system. This results in hard requirements on
performance which are not present in other simulators. Often they are either research tools with no no
performance requirements , or simulators for computer games or movies which may trade accuracy of
describing physical phenomena to improve performance. The Virtual testbed needs both accuracy and
performance, and this is the main difference that distinguishes it from similar programmes.
In [1] the authors develop a method for performing ship motion simulations based on physical
theories with simplifications that are necessary for real-time performance. These simplifications
include decomposition of the waves into head and transverse to speed-up calculation of wave
excitation forces. The authors mention that using velocity potential theory to compute these forces is
impractical to implement in real-time applications. Contrary to this statement we compute wave
excitation forces by computing velocity potentials. The reason that this approach works in real-time is
twofold. First, we use explicit formula based on Fourier transforms which is fast to compute compared
to implicit formulae that slower and needs numerical methods to compute. Second, we use GPU to
accelerate computations of Fourier transforms.
In [2] the authors use response amplitude operators to simulate ship motions in real-time. To
increase performance they also use fast Fourier transforms, but compute everything on CPU. Finally,
in [3] the authors study how GPU can be used to simulate ocean surface. In the Virtual testbed GPU is
used to improve performance of wavy surface generation, velocity potential and wave pressure
calculation.
3. Computation of external forces on GPU
The governing system of equations of ship motion is derived from the conservation laws for
mass and moment of inertia (second Newton's law), and are described in detail in various books on
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
ship dynamics [4,5]. The system of equations is solved numerically using fourth-order Runge—
Kutta—Fehlberg method. It is not the numerical method that consumes a lot of resources, but
calculation of external forces acting on the ship hull: buoyant force (due to pressure of water displaced
by the ship) and wave pressure force (due to ocean wave motion). Since the calculation of these forces
consumes most of the time required to render the frame, the code for computing them was rewritten
for GPU.
3.1. Velocity potential
Assuming that the fluid is incompressible and inviscid, we compute wave pressure from
velocity potentials. Velocity potential is determined from the following system of equations.
The first is the continuity (or Laplace) equation, the second is the equation of motion (or dynamic
boundary condition), the last one is a kinematic boundary condition on the free surface. Since the free
surface is known, the second equation becomes an explicit formula for wave pressure, and the problem
reduces to finding the velocity potential φ.
The system is solved using the Fourier method with some physical and mathematical
simplifications. The full solution is written as a convolution of some window function with
superposition of wavy surface derivatives. If we use the assumption of small-amplitude waves, the
solution is reduced to the solution from the linear wave theory.
Convolution is implemented as three Fourier transforms which makes it efficient to compute
on GPUs. The formula is suitable for any wavy surface regardless of the mathematical model used to
generate it as long as it is physically feasible: the same formula can be used for both plain and
irregular waves of arbitrary amplitude. Full derivation of the formula is given in [7].
3.2. Buoyant force
The buoyant force is proportional to the mass of the water displaced by the ship. In order to
compute it we decompose ship hull into triangular panels and determine underwater panels. For
partially submerged panels we compute their intersection with the water level (assuming that it is a
straight line) and consider only submerged part in the later computations. For each panel we compute
pressure due to water displacement and pressure due to ocean wave motion.
Then the force is simply a vector in the opposite direction of the surface normal to the panel
with length proportional to the pressure and panel area:
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
The total buoyant force is the sum of all individual forces acting on each submerged panel. If
one omits velocity potential terms, the formula becomes the Archimedes law for a single material
point. This algorithm has linear memory access pattern and involves a lot of floating point operations,
as well as vector arithmetic, which makes it efficient to implement on GPU.
4. Evaluation
The algorithms described in the previous section were implemented using OpenMP and
OpenCL, and using both CPU and GPU significantly improves performance compared to using only
CPU. We can see the performance difference between CPU and GPU implementation on the next
graphs. All tests were run on computer with AMD FX-8370 CPU and GeForce GTX 1060 6GB GPU.
Figure 1. Velocity potential computation Figure 2. External force computation
performance performance
The first experiment was to measure OpenMP implementation of velocity computation and
compare execution time with OpenCL implementation. As was mentioned, it uses three fast Fourier
transforms, that can be done very effectively on GPU [6]. So, thanks to this ability, OpenCL has better
performance. This fact is illustrated in Figure 1 that shows how performance scales with the number of
grid points.
The next test is similar to the previous one. We run the testbed with different frameworks to
compare time to compute pressures on ship hull. The wave pressure formula is easy to be parallelized
with OpenCL. Performance measurements are presented in Figure 2.
5. Discussion
We implement and test everything on CPU with OpenMP, and rewrite the programme hot-
spots in OpenCL. This allowed us to achieve approximately 30 frames per second on the target
machine. However, there is a room for improvement. We compute velocity potential derivatives on the
CPU which involves a lot of data copying between CPU and GPU memory. Also, we store ship hull
vertices and indices in CPU memory which causes even more data copying. In the future, we plan to
eliminate data copying overhead by storing everything in GPU memory and computing derivatives
using optimised OpenCL kernels.
In similar studies the authors often apply simplifications to the ship motion equations or
pressure computations formulae to achieve real-time performance. We choose to optimise only
computational part of the problem by offloading programme hot-spots to GPU. To optimise
mathematical part we use explicit formula for velocity potentials which works for any physically
feasible wavy surface. Thus, there is no restriction on mathematical model for ocean waves that can be
used in our programme.
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Proceedings of the VIII International Conference "Distributed Computing and Grid-technologies in Science and
Education" (GRID 2018), Dubna, Moscow region, Russia, September 10 - 14, 2018
6. Conclusion and future work
New implementation involves a lot of data copying between CPU and GPU memory, which
slowed the application a little bit. The next goal is to rewrite everything in OpenCL. This will further
speed-up computations and remove expensive data transfers.
Acknowledgements
The research was carried out within framework of grant of Saint Petersburg State University
no. 26520170.
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[4] Matusiak, J. Dynamics of a rigid ship //Helsinki: Aalto University, 2013
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