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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Field of algorithmic training</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Computer_engineering" title="Computer engineering">Computer engineering</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:LEAP_71_Noyron_TKL-5_Thruster.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/LEAP_71_Noyron_TKL-5_Thruster.jpg/220px-LEAP_71_Noyron_TKL-5_Thruster.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/72/LEAP_71_Noyron_TKL-5_Thruster.jpg/330px-LEAP_71_Noyron_TKL-5_Thruster.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/72/LEAP_71_Noyron_TKL-5_Thruster.jpg/440px-LEAP_71_Noyron_TKL-5_Thruster.jpg 2x" data-file-width="2048" data-file-height="1536" /></a><figcaption>5 kN rocket thruster built using a Computational Engineering Model using the PicoGK open-source library</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Kiva_Simulation.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Kiva_Simulation.jpg/200px-Kiva_Simulation.jpg" decoding="async" width="200" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/58/Kiva_Simulation.jpg 1.5x" data-file-width="225" data-file-height="219" /></a><figcaption>Simulation of an experimental engine</figcaption></figure> <p><b>Computational Engineering</b> is an emerging discipline that deals with the development and application of <a href="/wiki/Computational_model" title="Computational model">computational models</a> for engineering, known as Computational Engineering Models<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or CEM. Computational engineering uses computers to solve engineering design problems important to a variety of industries.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> At this time, various different approaches are summarized under the term Computational Engineering, including using <a href="/wiki/Computational_geometry" title="Computational geometry">computational geometry</a> and virtual design for engineering tasks,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> often coupled with a simulation-driven approach<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> In Computational Engineering, algorithms solve mathematical and logical models<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> that describe engineering challenges, sometimes coupled with some aspect of <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">AI</a>, specifically <a href="/wiki/Reinforcement_learning" title="Reinforcement learning">Reinforcement Learning</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In Computational Engineering the <a href="/wiki/Engineer" title="Engineer">engineer</a> encodes their knowledge using logical structuring. The result is an <a href="/wiki/Algorithm" title="Algorithm">algorithm</a>, the Computational Engineering Model, that can produce many different variants of engineering designs, based on varied input requirements. The results can then be analyzed through additional mathematical models to create algorithmic <a href="/wiki/Feedback" title="Feedback">feedback loops</a>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Physical_simulation" title="Physical simulation">Simulations of physical</a> behaviors relevant to the field, often coupled with <a href="/wiki/High-performance_computing" title="High-performance computing">high-performance computing</a>, to solve complex physical problems arising in engineering analysis and design (as well as natural phenomena (<a href="/wiki/Computational_science" title="Computational science">computational science</a>). It is therefore related to <a href="/wiki/Computational_Science_and_Engineering_Research_Journal" class="mw-redirect" title="Computational Science and Engineering Research Journal">Computational Science and Engineering</a>, which has been described as the "third mode of discovery" (next to theory and experimentation).<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>In Computational Engineering, <a href="/wiki/Computer_simulation" title="Computer simulation">computer simulation</a> provides the capability to create feedback that would be inaccessible to traditional experimentation or where carrying out traditional empirical inquiries is prohibitively expensive. </p><p>Computational Engineering should neither be confused with pure <a href="/wiki/Computer_science" title="Computer science">computer science</a>, nor with <a href="/wiki/Computer_engineering" title="Computer engineering">computer engineering</a>,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> although a wide domain in the former is used in Computational Engineering (e.g., certain algorithms, data structures, parallel programming, high performance computing) and some problems in the latter can be modeled and solved with Computational Engineering methods (as an application area). </p><p>It is typically offered as a <a href="/wiki/Master_of_Science" title="Master of Science">masters</a> or <a href="/wiki/Doctor_of_Philosophy" title="Doctor of Philosophy">doctorate</a> program.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Methods">Methods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_engineering&action=edit&section=1" title="Edit section: Methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Computational Engineering methods and frameworks include: </p> <ul><li><a href="/wiki/High_performance_computing" class="mw-redirect" title="High performance computing">High performance computing</a> and techniques to gain efficiency (through change in computer architecture, parallel algorithms etc.)</li> <li><a href="/wiki/Computer_model" class="mw-redirect" title="Computer model">Modeling</a> and <a href="/wiki/Simulation" title="Simulation">simulation</a></li> <li><a href="/wiki/Algorithms" class="mw-redirect" title="Algorithms">Algorithms</a> for solving discrete and continuous problems</li> <li>Analysis and visualization of data</li> <li>Mathematical foundations: Numerical and applied linear algebra, initial & boundary value problems, Fourier analysis, optimization</li> <li><a href="/wiki/Data_science" title="Data science">Data Science</a> for developing methods and algorithms to handle and extract knowledge from large scientific data</li></ul> <p>With regard to computing, computer programming, algorithms, and <a href="/wiki/Parallel_computing" title="Parallel computing">parallel computing</a> play a major role in Computational Engineering. The most widely used programming language in the scientific community is <a href="/wiki/FORTRAN" class="mw-redirect" title="FORTRAN">FORTRAN</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Recently, <a href="/wiki/C%2B%2B" title="C++">C++</a> and C have increased in popularity over FORTRAN. Due to the wealth of legacy code in FORTRAN and its simpler syntax, the scientific computing community has been slow in completely adopting C++ as the lingua franca. Because of its very natural way of expressing mathematical computations, and its built-in visualization capacities, the proprietary language/environment <a href="/wiki/MATLAB" title="MATLAB">MATLAB</a> is also widely used, especially for rapid application development and model verification. <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> along with external libraries (such as <a href="/wiki/NumPy" title="NumPy">NumPy</a>, <a href="/wiki/SciPy" title="SciPy">SciPy</a>, <a href="/wiki/Matplotlib" title="Matplotlib">Matplotlib</a>) has gained some popularity as a free and <a href="/wiki/Copycenter" class="mw-redirect" title="Copycenter">Copycenter</a> alternative to MATLAB. </p> <div class="mw-heading mw-heading2"><h2 id="Open_Source_Movement">Open Source Movement</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_engineering&action=edit&section=2" title="Edit section: Open Source Movement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>There are a number of Free and Open-Source Software (<a href="/wiki/Free_and_open-source_software" title="Free and open-source software">FOSS</a>) tools that support Computational Engineering. </p> <ul><li><a href="/wiki/OpenSCAD" title="OpenSCAD">OpenSCAD</a> was released in 2010 and allows the scripted generation of CAD models, which can form the basis for Computational Engineering Models.</li> <li><a rel="nofollow" class="external text" href="https://github.com/CadQuery/cadquery">CadQuery</a> uses <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> to generate <a href="/wiki/Computer-aided_design" title="Computer-aided design">CAD</a> models and is based on the <a href="/wiki/OpenSCAD" title="OpenSCAD">OpenSCAD</a> framework. It is released under the <a href="/wiki/Apache_License" title="Apache License">Apache 2.0 Open-Source License</a>.</li> <li><a rel="nofollow" class="external text" href="https://github.com/leap71/PicoGK">PicoGK</a>is an open-source framework for Computational Engineering which was released under the <a href="/wiki/Apache_License" title="Apache License">Apache 2.0 Open-Source License</a> in 2023 by LEAP 71, a Dubai-based company.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_engineering&action=edit&section=3" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Elmer-pump-heatequation.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Elmer-pump-heatequation.png/220px-Elmer-pump-heatequation.png" decoding="async" width="220" height="172" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Elmer-pump-heatequation.png/330px-Elmer-pump-heatequation.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Elmer-pump-heatequation.png/440px-Elmer-pump-heatequation.png 2x" data-file-width="1200" data-file-height="939" /></a><figcaption>A numerical solution to the <a href="/wiki/Heat_equation" title="Heat equation">heat equation</a> on a pump casing <a href="/wiki/Mathematical_model" title="Mathematical model">model</a> using the <a href="/wiki/Finite_element_method" title="Finite element method">finite element method</a>.</figcaption></figure> <p>Computational Engineering finds diverse applications, including in: </p> <ul><li><a href="/wiki/Aerospace_Engineering" class="mw-redirect" title="Aerospace Engineering">Aerospace Engineering</a> and <a href="/wiki/Mechanical_Engineering" class="mw-redirect" title="Mechanical Engineering">Mechanical Engineering</a>: <a href="/wiki/Combustion_models_for_CFD" title="Combustion models for CFD">combustion simulations</a>, <a href="/wiki/Structural_dynamics" title="Structural dynamics">structural dynamics</a>, <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamics</a>, <a href="/wiki/Computational_thermodynamics" title="Computational thermodynamics">computational thermodynamics</a>, computational solid mechanics, vehicle crash simulation, biomechanics, trajectory calculation of satellites</li> <li>Astrophysical systems</li> <li><a href="/wiki/Battle" title="Battle">Battlefield</a> simulations and military gaming, <a href="/wiki/Homeland_security" title="Homeland security">homeland security</a>, emergency response</li> <li><a href="/wiki/Biology" title="Biology">Biology</a> and <a href="/wiki/Medicine" title="Medicine">Medicine</a>: protein folding simulations (and other macromolecules), bioinformatics, genomics, computational neurological modeling, modeling of biological systems (e.g., ecological systems), 3D CT ultrasound, MRI imaging, molecular bionetworks, cancer and seizure control</li> <li><a href="/wiki/Chemistry" title="Chemistry">Chemistry</a>: calculating the structures and properties of chemical compounds/molecules and solids, <a href="/wiki/Computational_chemistry" title="Computational chemistry">computational chemistry</a>/cheminformatics, molecular mechanics simulations, computational chemical methods in solid state physics, chemical pollution transport</li> <li><a href="/wiki/Civil_Engineering" class="mw-redirect" title="Civil Engineering">Civil Engineering</a>: <a href="/wiki/Finite_element_analysis" class="mw-redirect" title="Finite element analysis">finite element analysis</a>, structures with random loads, construction engineering, water supply systems, transportation/vehicle modeling</li> <li><a href="/wiki/Computer_Engineering" class="mw-redirect" title="Computer Engineering">Computer Engineering</a>, <a href="/wiki/Electrical_Engineering" class="mw-redirect" title="Electrical Engineering">Electrical Engineering</a>, and <a href="/wiki/Telecommunications" title="Telecommunications">Telecommunications</a>: VLSI, computational electromagnetics, semiconductor modeling, simulation of microelectronics, energy infrastructure, RF simulation, networks</li> <li><a href="/wiki/Epidemiology" title="Epidemiology">Epidemiology</a>: influenza spread</li> <li><a href="/wiki/Environmental_Engineering" class="mw-redirect" title="Environmental Engineering">Environmental Engineering</a> and <a href="/wiki/Numerical_weather_prediction" title="Numerical weather prediction">Numerical weather prediction</a>: <a href="/wiki/Climate_research" class="mw-redirect" title="Climate research">climate research</a>, <a href="/wiki/Computational_geophysics" title="Computational geophysics">Computational geophysics</a> (seismic processing), modeling of natural disasters</li> <li><a href="/wiki/Finance" title="Finance">Finance</a>: derivative pricing, risk management</li> <li><a href="/wiki/Industrial_Engineering" class="mw-redirect" title="Industrial Engineering">Industrial Engineering</a>: discrete event and Monte-Carlo simulations (for logistics and manufacturing systems for example), queueing networks, <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">mathematical optimization</a></li> <li><a href="/wiki/Material_Science" class="mw-redirect" title="Material Science">Material Science</a>: glass manufacturing, polymers, and crystals</li> <li><a href="/wiki/Nuclear_Engineering" class="mw-redirect" title="Nuclear Engineering">Nuclear Engineering</a>: nuclear reactor modeling, radiation shielding simulations, fusion simulations</li> <li><a href="/wiki/Petroleum_engineering" title="Petroleum engineering">Petroleum engineering</a>: petroleum reservoir modeling, oil and gas exploration</li> <li><a href="/wiki/Physics" title="Physics">Physics</a>: Computational particle physics, automatic calculation of particle interaction or decay, plasma modeling, cosmological simulations</li> <li><a href="/wiki/Transportation" class="mw-redirect" title="Transportation">Transportation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_engineering&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Modeling_and_simulation" title="Modeling and simulation">Modeling and simulation</a></li> <li><a href="/wiki/Applied_mathematics" title="Applied mathematics">Applied mathematics</a></li> <li><a href="/wiki/Computational_science" title="Computational science">Computational science</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational mathematics</a></li> <li><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Computational fluid dynamics</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational electromagnetics</a></li> <li><a href="/wiki/High-performance_computing" title="High-performance computing">High-performance computing</a></li> <li><a href="/wiki/Engineering_mathematics" title="Engineering mathematics">Engineering mathematics</a></li> <li><a href="/wiki/Grand_Challenges" title="Grand Challenges">Grand Challenges</a></li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a></li> <li><a href="/wiki/Multiphysics" class="mw-redirect" title="Multiphysics">Multiphysics</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_engineering&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output 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0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20221221013602/https://ttu-ir.tdl.org/handle/2346/89584">"Computational Engineering Models for the Design of Mechanical Counterpressure Spacesuits"</a>. 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