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<li class="toctree-l1"><a class="reference internal" href="goveq.html">Governing equations</a></li>
<li class="toctree-l1"><a class="reference internal" href="goveq.html#semi-discrete-system">Semi-discrete System</a></li>
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<style> .red {color:red} </style><div class="section" id="shear-waves-shaw-simulator">
<h1>SHeAr Waves (SHAW) Simulator<a class="headerlink" href="#shear-waves-shaw-simulator" title="Permalink to this headline">¶</a></h1>
<p>This project contributes an open-source C++ code using the
Kokkos programming model to simulate the generation and propagation
of elastic shear waves in an axi-symmetric domain.</p>
<div class="figure align-center" id="id1">
<a class="reference internal image-reference" href="_images/logo1.png"><img alt="_images/logo1.png" src="_images/logo1.png" style="width: 26%;"/></a>
<p class="caption"><span class="caption-text">Sample countour plot of a velocity field obtained using the SHAW code.</span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
</div>
<div class="section" id="motivation">
<h2>Motivation<a class="headerlink" href="#motivation" title="Permalink to this headline">¶</a></h2>
<p>Seismic modeling and simulation is an active field of research
because of its critical importance to understand the generation,
propagation and effects of seismic events (aka earthquakes on Earth,
moonquakes on the moon, etc), and artificial explosions.</p>
<p>Broadly, one can distinguish between two main types
of seismic waves: shear and pressure.
Shear waves are also called S-waves (or secondary) because they come
after P-waves (or primary). The main difference is that S-waves
are <em>transversal</em> (particles oscillate perpendicularly to the direction
of wave propagation), while P-waves are <em>longitudinal</em> (particles oscillate
in the same direction as the wave). Both P- and S-waves
are body waves, because they travel through the interior of the Earth
(or some other planet), and their evolution is affected
by the generating source as well as the material properties of the medium,
namely density, stiffness, composition, etc.</p>
<p>Modeling and simulating these systems is challenging because (a) physical models
contain a large number of parameters (e.g., anisotropic material properties,
signal forms and parametrizations); and (b) simulating at global scale
with high-accuracy requires a large computational cost.</p>
<p>We hope our code can help advance this field and foster new research and related work.</p>
</div>
<div class="section" id="highlights-and-features">
<h2>Highlights and features<a class="headerlink" href="#highlights-and-features" title="Permalink to this headline">¶</a></h2>
<ul>
<li><p>Implementation based on the <a class="reference external" href="https://github.com/kokkos">Kokkos programming model</a>
for performance portability</p></li>
<li><p><a class="reference internal" href="goveq.html"><span class="doc">Velocity-stress formulation in an axi-symmetric domain</span></a></p></li>
<li><p>Support for the following material models:</p>
<ul class="simple">
<li><p><a class="reference internal" href="inputfile_description.html#singlelayerdescription"><span class="std std-ref">single layer model</span></a></p></li>
<li><p><a class="reference internal" href="inputfile_description.html#twolayerdescription"><span class="std std-ref">bilayer model</span></a></p></li>
<li><p><a class="reference internal" href="inputfile_description.html#premdescription"><span class="std std-ref">the Preliminary Reference Earth Model (PREM)</span></a></p></li>
<li><p><a class="reference internal" href="inputfile_description.html#customdescription"><span class="std std-ref">user-defined/custom model</span></a></p></li>
</ul>
<p>These are 1D models because they only depend on the radial distance.
The modularity of the code allows one to easily add new models</p>
</li>
<li><p>Simulating the dynamics in another planet/axisymmetric body is relatively easy:
you have to create a mesh suitable for that planet, and a suitable material model</p></li>
<li><p>The code implements what we refer to as “rank-1” and “rank-2” formulations:</p>
<ul class="simple">
<li><p><em>rank-1</em>:</p>
<ul>
<li><p><a class="reference internal" href="goveq.html#rank1fom"><span class="std std-ref">discrete state and forcing are stored as 1D arrays</span></a></p></li>
<li><p>this is useful to simulate the wave dynamics due to a <em>single forcing term</em></p></li>
<li><p><a class="reference internal" href="demo1.html"><span class="doc">See the demo!</span></a></p></li>
</ul>
</li>
<li><p><em>rank-2</em>:</p>
<ul>
<li><p><a class="reference internal" href="goveq.html#rank2fom"><span class="std std-ref">discrete state and forcing are stored using rank-2 tensors (i.e. matrices)</span></a></p></li>
<li><p>this is useful to <em>simultaneously</em> solve the wave
dynamics for <em>multiple forcing realizations</em> (e.g. multiple
source locations and/or periods). This rank-2 formulation
has an advantage from a computational standpoint because
it has higher computational intensity, thus benefiting
efficient ensemble propagation</p></li>
<li><p><a class="reference internal" href="demo3.html"><span class="doc">See the demo!</span></a></p></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
<div class="section" id="how-to-cite">
<h2>How to cite<a class="headerlink" href="#how-to-cite" title="Permalink to this headline">¶</a></h2>
<p>If you use this code, please cite the github page and the following paper:</p>
<div class="highlight-bibtex notranslate"><div class="highlight"><pre><span></span><span class="nc">@article</span><span class="p">{</span><span class="nl">RIZZI2021113973</span><span class="p">,</span>
<span class="na">title</span> <span class="p">=</span> <span class="s">{A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems}</span><span class="p">,</span>
<span class="na">journal</span> <span class="p">=</span> <span class="s">{Computer Methods in Applied Mechanics and Engineering}</span><span class="p">,</span>
<span class="na">volume</span> <span class="p">=</span> <span class="s">{384}</span><span class="p">,</span>
<span class="na">pages</span> <span class="p">=</span> <span class="s">{113973}</span><span class="p">,</span>
<span class="na">year</span> <span class="p">=</span> <span class="s">{2021}</span><span class="p">,</span>
<span class="na">issn</span> <span class="p">=</span> <span class="s">{0045-7825}</span><span class="p">,</span>
<span class="na">doi</span> <span class="p">=</span> <span class="s">{https://doi.org/10.1016/j.cma.2021.113973}</span><span class="p">,</span>
<span class="na">url</span> <span class="p">=</span> <span class="s">{https://www.sciencedirect.com/science/article/pii/S0045782521003042}</span><span class="p">,</span>
<span class="na">author</span> <span class="p">=</span> <span class="s">{Francesco Rizzi and Eric J. Parish and Patrick J. Blonigan and John Tencer}</span>
<span class="p">}</span>
</pre></div>
</div>
</div>
</div>
<div class="section" id="contents">
<h1>Contents<a class="headerlink" href="#contents" title="Permalink to this headline">¶</a></h1>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="goveq.html">Governing equations</a></li>
<li class="toctree-l1"><a class="reference internal" href="goveq.html#semi-discrete-system">Semi-discrete System</a></li>
<li class="toctree-l1"><a class="reference internal" href="goveq.html#time-integration">Time integration</a></li>
<li class="toctree-l1"><a class="reference internal" href="build_expert.html">Building: “expert” mode</a><ul>
<li class="toctree-l2"><a class="reference internal" href="build_expert.html#prerequisites">Prerequisites</a></li>
<li class="toctree-l2"><a class="reference internal" href="build_expert.html#build">Build</a></li>
</ul>
</li>
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<li class="toctree-l2"><a class="reference internal" href="build_stepbystep.html#prerequisites">Prerequisites</a></li>
<li class="toctree-l2"><a class="reference internal" href="build_stepbystep.html#step-1-prepare-environment">Step 1: Prepare environment</a></li>
<li class="toctree-l2"><a class="reference internal" href="build_stepbystep.html#step-2-build-tpls">Step 2: Build TPLs</a></li>
<li class="toctree-l2"><a class="reference internal" href="build_stepbystep.html#step-3-build-shaw">Step 3: Build SHAW</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="inputfile.html">Input File</a><ul>
<li class="toctree-l2"><a class="reference internal" href="inputfile_description.html">General Section</a></li>
<li class="toctree-l2"><a class="reference internal" href="inputfile_description.html#io-section">IO Section</a></li>
<li class="toctree-l2"><a class="reference internal" href="inputfile_description.html#source-forcing-section">Source/forcing Section</a></li>
<li class="toctree-l2"><a class="reference internal" href="inputfile_description.html#material-model-section">Material Model Section</a></li>
<li class="toctree-l2"><a class="reference internal" href="inputfile_template.html">Template</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="demos.html">End-to-end Demos</a><ul>
<li class="toctree-l2"><a class="reference internal" href="demo1.html">Demo 1</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo2.html">Demo 2</a></li>
<li class="toctree-l2"><a class="reference internal" href="demo3.html">Demo 3</a></li>
</ul>
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