commit ebb4fbdbbc980ef7151d03cf400fe0a16098f9f2
parent 0e832262c8157f4096ded6f5313571d8e3a981c8
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Tue, 13 Jun 2017 11:28:27 +0300
Replace ocean waves with sea waves.
Diffstat:
2 files changed, 62 insertions(+), 62 deletions(-)
diff --git a/arma-thesis-ru.org b/arma-thesis-ru.org
@@ -300,7 +300,7 @@ NaN: 29, -nan, 1.798e+36, -1.04284e+38, inf, -1.798e+36, -1.798e+36
исходный код программы.
2. /Линейность/. В рамках линейной теории волн дается математическое определение
морским волнам в предположении малости их амплитуд по сравнению с длинами.
- Такие волны, в основном, характерны для открытого моря и океана, а волны в
+ Такие волны, в основном, характерны для открытого океана, а волны в
прибрежных районах и штормовые волны, для которых это предположение
несправедливо, грубо описываются в рамках линейной теории.
3. /Вероятностная сходимость/. Фаза волны, значение которой обычно получается с
diff --git a/arma-thesis.org b/arma-thesis.org
@@ -9,7 +9,7 @@
# eval: (add-to-list 'org-latex-classes '("gost" "\\documentclass{gost} [DEFAULT-PACKAGES] [PACKAGES] [EXTRA]" ("\\section{%s}" . "\\section*{%s}") ("\\subsection{%s}" . "\\subsection*{%s}") ("\\subsubsection{%s}" . "\\subsubsection*{%s}") ("\\paragraph{%s}" . "\\paragraph*{%s}") ("\\subparagraph{%s}" . "\\subparagraph*{%s}")))
# End:
-#+TITLE: High-performance ocean wave simulation model for studying marine object behaviour
+#+TITLE: High-performance sea wave simulation model for studying marine object behaviour
#+AUTHOR: Ivan Gankevich
#+DATE: St. Petersburg, 2017
#+LANGUAGE: en
@@ -1200,7 +1200,7 @@ Zeta size = (192,32,32)
Software programmes, which simulates vessel behaviour in sea waves, are widely
used to model ship motion, estimate impact of external forces on floating
platform or other marine object, and estimate capsize probability under given
-weather conditions; however, to model ocean waves most of the simulation codes
+weather conditions; however, to model sea waves most of the simulation codes
use linear wave theory\nbsp{}cite:shin2003nonlinear,van2007forensic,kat2001prediction,van2002development, in
the framework of which it is difficult to reproduce certain peculiarities of
wind wave climate. Among them are transition between normal and storm weather,
@@ -1209,7 +1209,7 @@ heading from multiple directions. Another shortcoming of linear wave theory is
an assumption, that wave amplitude is small compared to wave length. This makes
calculations imprecise when modelling ship motion in irregular waves, for which
the assumption does not hold. So, studying new and more advanced models and
-methods for ocean simulation software may increase number of its application
+methods for sea simulation software may increase number of its application
scenarios and foster a study of ship motion in extreme conditions in particular.
**** State-of-the-art.
@@ -1225,9 +1225,9 @@ can be summarised as the following.
non-linearly with realisation size. This in turn results in overall low
efficiency of any model based on this theory, no matter how optimised the
software implementation is.
-2. /Linearity/. Linear wave theory gives mathematical definition for ocean waves
+2. /Linearity/. Linear wave theory gives mathematical definition for sea waves
which have small amplitudes compared to their lengths. Waves of this type
- occur mostly in the ocean, so near-shore waves as well as storm waves, for
+ occur mostly in open ocean, so near-shore waves as well as storm waves, for
which this assumption does not hold, are not perfectly captured by linear
theory.
3. /Probabilistic convergence/. Phase of a wave, which is often generated by
@@ -1245,14 +1245,14 @@ required mathematical apparatus.
frequency-directional spectrum (which is the input for Longuet---Higgins
model). So, inputs for one model can easily be converted to each other.
2. There is no small-amplitude waves assumption. Wave may have any amplitude,
- and can be generated as steep as it is possible with real ocean wave ACF.
+ and can be generated as steep as it is possible with real sea wave ACF.
3. Period of the realisation equals the period of PRNG, so generation time grows
linearly with the realisation size.
4. White noise\nbsp{}--- the only probabilistic term in ARMA process\nbsp{}--- has
Gaussian distribution; so, convergence rate is not probabilistic.
**** Goals and objectives.
-ARMA process became the basis for ARMA ocean simulation model, however, there
+ARMA process became the basis for ARMA sea simulation model, however, there
was still much work to be done to make it useful in practice.
1. One have to investigate how different ACF shapes affect the choice of ARMA
parameters (the number of moving average and autoregressive processes
@@ -1267,13 +1267,13 @@ was still much work to be done to make it useful in practice.
general wavy surface (which is not defined by an analytic formula),
without linearisation of boundaries and assumption of small-amplitude waves.
4. Finally, verify wavy surface integral characteristics to match the ones of
- real ocean waves.
+ real sea waves.
5. In the final stage, develop software programme that implements ARMA model and
pressure calculation method, and allows to run simulations on both shared
memory (SMP) and distributed memory (MPP) computer systems.
**** Scientific novelty.
-ARMA model, as opposed to other ocean simulation models, does not use linear
+ARMA model, as opposed to other sea simulation models, does not use linear
wave theory. This makes it capable of
- generating waves with arbitrary amplitudes by adjusting wave steepness via
ACF;
@@ -1327,7 +1327,7 @@ programming language allowing visual control of programme correctness.
**** Results verification and approbation.
ARMA model is verified by comparing generated wavy surface integral
characteristics (distribution of wave elevation, wave heights and lengths etc.)
-to the ones of real ocean waves. Pressure field formula is derived in
+to the ones of real sea waves. Pressure field formula is derived in
Mathematica language, where resulting formulae are verified by built-in
graphical means.
@@ -1338,13 +1338,13 @@ experiments showed higher computational efficiency of ARMA model.
* Problem statement
The aim of the study reported here is to investigate possibilities of applying
-ARMA process mathematical apparatus to ocean wave modelling and to derive formula
+ARMA process mathematical apparatus to sea wave modelling and to derive formula
for pressure field under generated wavy surface without assumptions of linear
wave theory.
- In case of small-amplitude waves resulting formula must correspond to the
one from linear wave theory; in all other cases the formula must not diverge.
- Integral characteristics of generated wavy surface must match the ones of real
- ocean waves.
+ sea waves.
- Software implementation of ARMA model and pressure field formula must work on
shared memory (SMP) and distributed memory (MPP) systems.
@@ -1378,7 +1378,7 @@ inverse problem of hydrodynamics reduces to Laplace equation with mixed boundary
condition\nbsp{}--- Robin problem.
* Related work
-** Ocean wave models analysis
+** Sea wave models analysis
Pressure computation is only possible when the shape of wavy surface is known.
It is defined either at discrete grid points, or continuously via some analytic
formula. As will be shown in section [[#linearisation]], such formula may simplify
@@ -1392,7 +1392,7 @@ Longuet---Higgins (LH) model\nbsp{}cite:longuet1957statistical. In-depth
comparative analysis of this model and ARMA model is done
in\nbsp{}cite:degtyarev2011modelling,boukhanovsky1997thesis.
-LH model represents ocean wavy surface as a superposition of
+LH model represents sea wavy surface as a superposition of
sine waves with random amplitudes \(c_n\) and phases \(\epsilon_n\), continuously
distributed on interval \([0,2\pi]\). Wavy surface elevation (\(z\) coordinate) is
defined by
@@ -1424,7 +1424,7 @@ appear in practice.
used as the model input. Using lower number of coefficients may solve the
problem, but also make realisation period smaller. So, using LH model to
simulate waves with non-Gaussian distribution of elevation\nbsp{}--- a
- distribution which real ocean waves
+ distribution which real sea waves
have\nbsp{}cite:huang1980experimental,рожков1996теория \nbsp{}--- is
impractical.
2. From computational point of view, the deficiency of the model is non-linear
@@ -1442,13 +1442,13 @@ appear in practice.
which there is no known formula to determine
coefficients\nbsp{}cite:рожков1990вероятностные.
-To summarise, LH model is applicable to generating ocean wavy surface in the
+To summarise, LH model is applicable to generating sea wavy surface in the
framework of linear wave theory, inefficient for long-time simulations, and
difficult to use as a base for more advanced models.
**** ARMA model
In\nbsp{}cite:spanos1982arma ARMA model is used to generate time series spectrum of
-which is compatible with Pierson---Moskowitz (PM) approximation of ocean wave
+which is compatible with Pierson---Moskowitz (PM) approximation of sea wave
spectrum. The authors carry out experiments for one-dimensional AR, MA and ARMA
models. They mention excellent agreement between target and initial spectra and
higher performance of ARMA model compared to models based on summing large
@@ -1467,24 +1467,24 @@ is mostly a different problem.
determined manually.
3. Instead of PM spectrum, analytic formulae for standing and propagating
waves ACF are used as the model input.
-4. Three-dimensional wavy surface should be compatible with real ocean surface
+4. Three-dimensional wavy surface should be compatible with real sea surface
not only in terms of spectral characteristics, but also in the shape of wave
profiles. So, model verification includes distributions of various parameters
of generated waves (lengths, heights, periods etc.).
Multi-dimensionality of investigated model not only complexifies the task, but
also allows to carry out visual validation of generated wavy surface. It is the
opportunity to visualise output of the programme that allowed to ensure that
-generated surface is compatible with real ocean surface, and is not abstract
+generated surface is compatible with real sea surface, and is not abstract
multi-dimensional stochastic process that is real only statistically.
In\nbsp{}cite:fusco2010short AR model is used to predict swell waves to control
wave-energy converters (WEC) in real-time. In order to make WEC more efficient
-its internal oscillator frequency should match the one of ocean waves. The
+its internal oscillator frequency should match the one of sea waves. The
authors treat wave elevation as time series and compare performance of AR model,
neural networks and cyclical models in forecasting time series future values. AR
model gives the most accurate prediction of low-frequency swell waves for up to
two typical wave periods. It is an example of successful application of AR
-process to ocean wave modelling.
+process to sea wave modelling.
** Pressure field determination formulae
**** Small amplitude waves theory.
@@ -1550,9 +1550,9 @@ This formula is differentiated to obtain velocity potential derivatives, which
are plugged to dynamic boundary condition to obtain pressures.
-* ARMA model for ocean wave simulation
+* ARMA model for sea wave simulation
** Governing equations for 3-dimensional ARMA process
-ARMA ocean simulation model defines ocean wavy surface as three-dimensional (two
+ARMA sea simulation model defines sea wavy surface as three-dimensional (two
dimensions in space and one in time) autoregressive moving average process:
every surface point is represented as a weighted sum of previous in time and
space points plus weighted sum of previous in time and space normally
@@ -1784,13 +1784,13 @@ is to simply use AR and MA process exclusively.
:CUSTOM_ID: sec-process-selection
:END:
-One problem of ARMA model application to ocean wave generation is that for
+One problem of ARMA model application to sea wave generation is that for
different types of wave profiles different processes /must/ be used: standing
waves are modelled by AR process, and propagating waves by MA process. This
statement comes from practice: if one tries to use the processes the other way
round, the resulting realisation either diverges or does not correspond to real
-ocean waves. (The latter happens for non-invertible MA process, as it is always
-stationary.) So, the best way to apply ARMA model to ocean wave generation is to
+sea waves. (The latter happens for non-invertible MA process, as it is always
+stationary.) So, the best way to apply ARMA model to sea wave generation is to
use AR process for standing waves and MA process for progressive waves.
The other problem is inability to automatically determine optimal number of
@@ -1806,14 +1806,14 @@ should be flipped for three-dimensional case. For example, the authors say that
ACF of MA process cuts at \(q\) and ACF of AR process decays to nought infinitely,
but in practice making ACF of 3-dimensional MA process not decay results in it
being non-invertible and producing realisation that does not look like real
-ocean waves, whereas doing the same for ACF of AR process results in stationary
+sea waves, whereas doing the same for ACF of AR process results in stationary
process and adequate realisation. Also, the authors say that one
should allocate the first \(q\) points of ACF to MA process (as it often needed to
describe the peaks in ACF) and leave the rest points to AR process, but in
practice in case of ACF of a propagating wave AR process is stationary only for
the first time slice of the ACF, and the rest is left to MA process.
-To summarise, the only established scenario of applying ARMA model to ocean wave
+To summarise, the only established scenario of applying ARMA model to sea wave
generation is to use AR process for standing waves and MA process for
propagating waves. With new formulae for 3 dimensions a single mixed ARMA
process might increase model precision, which is one of the objectives of the
@@ -1856,7 +1856,7 @@ Second, there are implementations of FFT optimised for different processor
architectures as well as co-processors (GPU, MIC) which makes it easy to get
high performance on any computing platform. These advantages substantiate the
choice of Fourier method to obtain explicit analytic solution to the problem of
-determining pressures under wavy ocean surface.
+determining pressures under wavy sea surface.
*** Two-dimensional velocity field
:PROPERTIES:
@@ -2148,10 +2148,10 @@ and plugging the result into eqref:eq-guessed-sol-3d yields formula for
\end{equation*}
where \(\FourierY{\mathcal{D}_3\left(x,y,z\right)}{u,v}=\Sinh{\smash{2\pi\Kveclen{}z}}\).
-** Modelling non-linearity of ocean waves
+** Modelling non-linearity of sea waves
ARMA model allows to model asymmetry of wave elevation distribution, i.e.\nbsp{}
-generate ocean waves, distribution of \(z\)-coordinate of which has non-nought
-kurtosis and asymmetry. Such distribution is inherent to real ocean
+generate sea waves, distribution of \(z\)-coordinate of which has non-nought
+kurtosis and asymmetry. Such distribution is inherent to real sea
waves\nbsp{}cite:longuet1963nonlinear.
Wave asymmetry is modelled by non-linear inertia-less transform (NIT) of
@@ -2218,7 +2218,7 @@ fields become equal with desired accuracy \(\epsilon\):
In\nbsp{}cite:boukhanovsky1997thesis the author suggests using polynomial
approximation \(f(y)\) also for wavy surface transformation, however, in
-practice ocean surface realisation often contains points, where \(z\)-coordinate
+practice sea surface realisation often contains points, where \(z\)-coordinate
is beyond the limits of the approximation, which makes solution invalid. In
these points it is more efficient to solve equation
eqref:eq-distribution-transformation by bisection method. Using the same
@@ -2230,7 +2230,7 @@ approximation in Gram---Charlier series does not lead to such errors.
:CUSTOM_ID: sec-wave-acfs
:END:
**** Analytic method of finding the ACF.
-The straightforward way to find ACF for a given ocean wave profile is to apply
+The straightforward way to find ACF for a given sea wave profile is to apply
Wiener---Khinchin theorem. According to this theorem the autocorrelation \(K\) of
a function \(\zeta\) is given by the Fourier transform of the absolute square of
the function:
@@ -2318,7 +2318,7 @@ exponent without need to adapt the maximum value of ACF (as it is required for
standing wave).
**** Comparison of studied methods.
-To summarise, the analytic method of finding ocean wave's ACF reduces to the
+To summarise, the analytic method of finding sea wave's ACF reduces to the
following steps.
- Make wave profile decay when approaching \(\pm\infty\) by multiplying it by
a decaying exponent.
@@ -2341,7 +2341,7 @@ steps.
:CUSTOM_ID: sec:arma-algorithms
:END:
*** Wave elevation distribution approximation
-One of the parameters of ocean wavy surface generator is probability density
+One of the parameters of sea wavy surface generator is probability density
function (PDF) of the surface elevation. This distribution is given by either
polynomial approximation of /in situ/ data or analytic formula.
@@ -2369,7 +2369,7 @@ of PDF expands in Gram---Charlier series:
where \(\Phi(z)\)\nbsp{}--- CDF of normal distribution, \(\phi\)\nbsp{}--- PDF
of normal distribution, \(\gamma_1\)\nbsp{}--- skewness, \(\gamma_2\)\nbsp{}---
kurtosis, \(f\)\nbsp{}--- PDF, \(F\)\nbsp{}--- cumulative distribution function
-(CDF). According to\nbsp{}cite:рожков1990вероятностные for ocean waves skewness
+(CDF). According to\nbsp{}cite:рожков1990вероятностные for sea waves skewness
is selected from interval \(0.1\leq\gamma_1\leq{0.52}]\) and kurtosis from
interval \(0.1\leq\gamma_2\leq{0.7}\). Family of probability density functions
for different parameters is shown in fig.\nbsp{}[[fig-skew-normal-1]].
@@ -2400,13 +2400,13 @@ legend(
)
#+end_src
-#+caption: Probability density function eqref:eq-skew-normal-1 of ocean wavy surface elevation for different values of skewness \(\gamma_1\) and kurtosis \(\gamma_2\).
+#+caption: Probability density function eqref:eq-skew-normal-1 of sea wavy surface elevation for different values of skewness \(\gamma_1\) and kurtosis \(\gamma_2\).
#+label: fig-skew-normal-1
#+RESULTS: fig-skew-normal-1
[[file:build/skew-normal-1.pdf]]
**** Skew-normal distribution.
-Alternative approach is to approximate distribution of ocean wavy surface
+Alternative approach is to approximate distribution of sea wavy surface
elevation by skew-normal distribution:
\begin{align}
\label{eq-skew-normal-2}
@@ -2452,7 +2452,7 @@ legend(
)
#+end_src
-#+caption: Probability density function eqref:eq-skew-normal-2 of ocean wavy surface for different values of skewness coefficient \(\alpha\).
+#+caption: Probability density function eqref:eq-skew-normal-2 of sea wavy surface for different values of skewness coefficient \(\alpha\).
#+label: fig-skew-normal-2
#+RESULTS: fig-skew-normal-2
[[file:build/skew-normal-2.pdf]]
@@ -2474,7 +2474,7 @@ transform ACF; relative error without interpolation is \(10^{-5}\).
In order to eliminate periodicity from generated wavy surface, it is imperative
to use PRNG with sufficiently large period to generate white noise. Parallel
Mersenne Twister\nbsp{}cite:matsumoto1998mersenne with a period of \(2^{19937}-1\) is
-used as a generator in this work. It allows to produce aperiodic ocean wavy
+used as a generator in this work. It allows to produce aperiodic sea wavy
surface realisations in any practical usage scenarios.
There is no guarantee that multiple Mersenne Twisters executed in parallel
@@ -2501,7 +2501,7 @@ ship stability with manoeuvring is studied, then the interval may be simply
discarded from the realisation (the size of the interval approximately equals
the number of AR coefficients in each dimension). However, this may lead to loss
of a very large number of points, because discarding occurs for each dimension.
-Alternative approach is to generate ocean wavy surface on ramp-up interval with
+Alternative approach is to generate sea wavy surface on ramp-up interval with
LH model and generate the rest of the realisation with ARMA model.
Algorithm of wavy surface generation is data-parallel: realisation is divided
@@ -2573,7 +2573,7 @@ In this work both AR and MA model are verified by comparing probability
distributions of different wave characteristics.
*** Verification of wavy surface integral characteristics
-In\nbsp{}cite:рожков1990вероятностные the authors show that several ocean wave
+In\nbsp{}cite:рожков1990вероятностные the authors show that several sea wave
characteristics (listed in table\nbsp{}[[tab-weibull-shape]]) have Weibull distribution,
and wavy surface elevation has Gaussian distribution. In order to verify that
distributions corresponding to generated realisation are correct,
@@ -2668,7 +2668,7 @@ Correspondence rate for standing waves (fig.\nbsp{}[[standing-wave-distributions
is lower for height and length, roughly the same for surface
elevation and higher for wave period distribution tails. Lower correspondence
degree for length and height may be attributed to the fact that Weibull
-distributions were obtained empirically for ocean waves which are typically
+distributions were obtained empirically for sea waves which are typically
propagating, and distributions may be different for standings waves. Higher
correspondence degree for wave periods is attributed to the fact that wave
periods of standing waves are extracted more precisely as the waves do not move
@@ -2688,7 +2688,7 @@ plain waves, so comparison is done numerically. Taking into account conclusions
of [[#sec:pressure-2d]], only finite depth formulae are compared.
**** The difference with linear wave theory formulae.
-In order to obtain velocity potential fields, ocean wavy surface was generated
+In order to obtain velocity potential fields, sea wavy surface was generated
by AR model with varying wave amplitude. In numerical implementation wave
numbers in Fourier transforms were chosen on the interval from \(0\) to the
maximal wave number determined numerically from the obtained wavy surface.
@@ -2757,7 +2757,7 @@ arma.plot_velocity_potential_field_legend(
The experiment, in which velocity fields produced numerically by different
formulae were compared, shows that velocity fields produced by formula
eqref:eq-solution-2d-full and eqref:eq-old-sol-2d correspond to each other for
-small-amplitude waves. Two ocean wavy surface realisations were made by AR
+small-amplitude waves. Two sea wavy surface realisations were made by AR
model: one containing small-amplitude waves, other containing large-amplitude
waves. Integration in formula eqref:eq-solution-2d-full was done over wave
numbers range extracted from the generated wavy surface. For small-amplitude
@@ -2789,7 +2789,7 @@ arma.plot_velocity(
#+end_src
#+label: fig-velocity-field-2d
-#+caption: Comparison of velocity field on the ocean wavy surface obtained by generic formula (\(u_1\)) and formula for small-amplitude waves (\(u_2\)). Velocity field for realisations containing small-amplitude (top) and large-amplitude (bottom) waves.
+#+caption: Comparison of velocity field on the sea wavy surface obtained by generic formula (\(u_1\)) and formula for small-amplitude waves (\(u_2\)). Velocity field for realisations containing small-amplitude (top) and large-amplitude (bottom) waves.
#+attr_latex: :width \textwidth
#+RESULTS: fig-velocity-field-2d
[[file:build/large-and-small-amplitude-velocity-field-comparison.pdf]]
@@ -2886,18 +2886,18 @@ ascii(result)
#+END_SRC
*** Non-physical nature of ARMA model
-ARMA model, owing to its non-physical nature, does not have the notion of ocean
+ARMA model, owing to its non-physical nature, does not have the notion of sea
wave; it simulates wavy surface as a whole instead. Motions of individual waves
and their shape are often rough, and the total number of waves can not be
determined precisely. However, integral characteristics of wavy surface match
-the ones of real ocean waves.
+the ones of real sea waves.
-Theoretically, ocean waves themselves can be chosen as ACFs, the only
+Theoretically, sea waves themselves can be chosen as ACFs, the only
pre-processing step is to make them decay exponentially. This may allow
to generate waves of arbitrary profiles, and is one of the directions of future
work.
-* High-performance software implementation of ocean wave simulation
+* High-performance software implementation of sea wave simulation
** Computational model
**** Mapping wavy surface generation algorithm on computational model.
Software implementation of ARMA model works as a computational pipeline, in
@@ -2955,7 +2955,7 @@ digraph {
end [label="",shape=doublecircle,style=filled,fillcolor=black,width=0.23]
generate_white_noise [label="<g1> g₁|<g2> g₂|<g3> …|<g4> gₙ|<gen> Generate\lwhite noise",shape=record,style=rounded]
- generate_zeta [label="<g1> g₁|<g2> g₂|<g3> …|<g4> gₙ|<gen> Generate ocean\lwavy surface parts\l",shape=record,style=rounded]
+ generate_zeta [label="<g1> g₁|<g2> g₂|<g3> …|<g4> gₙ|<gen> Generate sea\lwavy surface parts\l",shape=record,style=rounded]
zeta_parts [label="<g1> ζ₁|<g2> ζ₂|<g3> …|<g4> ζₙ|<gen> Non-crosslinked\lrealisation parts",shape=record]
overlap_add [label="<g1> ζ₁|<g2> ζ₂|<g3> …|<g4> ζₙ|<gen> Crosslink realisation\lparts\l",shape=record,style=rounded]
@@ -3020,7 +3020,7 @@ digraph {
}
#+end_src
-#+caption: Diagram of data processing pipeline, that implements ocean wavy surface generation via AR model.
+#+caption: Diagram of data processing pipeline, that implements sea wavy surface generation via AR model.
#+label: fig-pipeline
#+RESULTS: fig-pipeline
[[file:build/pipeline.pdf]]
@@ -3039,7 +3039,7 @@ and their parallel usage increases the whole programme performance.
Since data transfer between pipeline joints is done in parallel to computations,
the same pipeline may be used to run several copies of the application but with
-different parameters (generate several ocean wavy surfaces having different
+different parameters (generate several sea wavy surfaces having different
characteristics). In practise, high-performance applications do not always
consume 100% of processor time spending a portion of time on synchronisation of
parallel processes and writing data to disk. Using pipeline in this case allows
@@ -3933,7 +3933,7 @@ An example of fail over algorithm follows (fig.\nbsp{}[[fig-fail-over-example]])
**** Evaluation results.
Factory framework is evaluated on physical cluster (table\nbsp{}[[tab-cluster]]) on the
-example of HPC application, that generates ocean wavy surface, which is
+example of HPC application, that generates sea wavy surface, which is
described in detail in section [[#sec:arma-algorithms]]. The application consists of
a series of filters, each of which is applied to the result of the previous one.
Some of the filters are computed in parallel, so the programme is written as a
@@ -4114,7 +4114,7 @@ automatic fault-tolerance. Programmes written with MPI typically assume
- non-interruptible and reliable execution of batch jobs, and
- constant number of parallel processes/threads throughout the execution which
is equal to the total number of processors.
-The first assumption does not hold for ocean wave simulation programme because
+The first assumption does not hold for sea wave simulation programme because
AR model requires dynamic load balancing between processors to generate each
part of the surface only when all dependent parts has already been generated.
The last assumption also does not hold, because for the sake of efficiency each
@@ -4156,7 +4156,7 @@ entities. First, this allows to determine the number of entities computed in
parallel by the problem being solved, not the computer or cluster architecture.
A programmer is encouraged to create as many objects as needed, guided by the
algorithm or restrictions on the size of data structures from the problem
-domain. In ocean wave simulation programme the minimal size of each wavy surface
+domain. In sea wave simulation programme the minimal size of each wavy surface
part depends on the number of coefficients along each dimension, and at the same
time the number of parts should be larger than the number of processors to make
the load on each processor more even. Considering these limits the optimal part
@@ -4196,11 +4196,11 @@ without interruption.
* Conclusion
**** Research results.
-In the sutdy of matheamtical apparatus for ocean wave simulations which goes
+In the sutdy of matheamtical apparatus for sea wave simulations which goes
beyond linear wave theory the following main results were achieved.
-- ARMA model was applied to simulation of ocean waves of arbitrary amplitudes.
+- ARMA model was applied to simulation of sea waves of arbitrary amplitudes.
Integral characteristics of generated wavy surface were verified by comparing
- to the ones of a real ocean surface.
+ to the ones of a real sea surface.
- Analytic formula for determining wave pressures was applied to compute
velocity potentials under generated surface. The resulting velocity potential
field was verified by comparing it to the one given by fromuale from linear
@@ -4218,7 +4218,7 @@ software packages.
* Summary
Research results allow to conclude that a problem of determining pressures under
sea surface can be solved analytically without assumptions of linear and
-small-amplitude wave theories. This solution coupled with ARMA ocean wave
+small-amplitude wave theories. This solution coupled with ARMA sea wave
simulation model, capable of generating waves of arbitrary amplitudes, can be
used to determine the impact of wave oscillations on the dynamic marine object
in a sea way, and give more precise results than analogous solution for
