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docs/absorption_8hpp.html

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<div class="textblock"><code>#include &lt;thread&gt;</code><br />
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<code>#include &quot;<a class="el" href="newton_8hpp_source.html">newton.hpp</a>&quot;</code><br />
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<code>#include &quot;<a class="el" href="output_8hpp_source.html">output.hpp</a>&quot;</code><br />
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<code>#include &quot;<a class="el" href="dispersion_8hpp_source.html">dispersion.hpp</a>&quot;</code><br />
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</div>
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<p><a href="absorption_8hpp_source.html">Go to the source code of this file.</a></p>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="nested-classes" name="nested-classes"></a>
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Classes</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classabsorption_1_1method.html">absorption::method&lt; T, SAFE_MATH &gt;</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Base class for absoption models. <a href="classabsorption_1_1method.html#details">More...</a><br /></td></tr>
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<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Base class for absorption models. <a href="classabsorption_1_1method.html#details">More...</a><br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classabsorption_1_1root__finder.html">absorption::root_finder&lt; T, SAFE_MATH &gt;</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Class interface for the root finder. <a href="classabsorption_1_1root__finder.html#details">More...</a><br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Base class for an absorption model. </p>
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<p>Defines functions for computing power absorbtion. </p>
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<p>Defines functions for computing power absorption. </p>
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</div></div><!-- contents -->
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docs/absorption_8hpp_source.html

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docs/absorption_model.html

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<meta http-equiv="X-UA-Compatible" content="IE=11"/>
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<meta name="generator" content="Doxygen 1.9.8"/>
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<meta name="viewport" content="width=device-width, initial-scale=1"/>
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<title>Graph Framework: Absoption Models</title>
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<title>Graph Framework: Absorption Models</title>
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<link href="tabs.css" rel="stylesheet" type="text/css"/>
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<div><div class="header">
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<div class="headertitle"><div class="title">Absoption Models</div></div>
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<div class="headertitle"><div class="title">Absorption Models</div></div>
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</div><!--header-->
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<div class="contents">
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<div class="toc"><h3>Table of Contents</h3>
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<ul><li class="level1"><a href="#absorption_model_intro">Introduction</a><ul><li class="level2"><a href="#absorption_model_hot">Hot Plasma Disperison Function</a><ul><li class="level3"><a href="#absorption_model_hotexpand">Expansion Terms</a></li>
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<ul><li class="level1"><a href="#absorption_model_intro">Introduction</a><ul><li class="level2"><a href="#absorption_model_hot">Hot Plasma Dispersion Function</a><ul><li class="level3"><a href="#absorption_model_hotexpand">Expansion Terms</a></li>
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</ul>
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</li>
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</ul>
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<li class="level1"><a href="#absorption_model_devel">Developing new absorption models</a></li>
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</ul>
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</div>
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<div class="textblock"><p>A discription of the models for power absorption.</p>
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<div class="textblock"><p>A description of the models for power absorption.</p>
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<h1><a class="anchor" id="absorption_model_intro"></a>
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Introduction</h1>
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<p>This page documents the types of dispersion functions available. Tracing the ray is only the first step in the process. Along that, ray power is deposited into the plasma. For tracing the ray we assumed the wave number was always real. However, now we need to figure out what the imaginary component is.</p>
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<h2><a class="anchor" id="absorption_model_hot"></a>
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Hot Plasma Disperison Function</h2>
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Hot Plasma Dispersion Function</h2>
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<p>To do this we now assume a hot plasma dispersion function. </p><p class="formulaDsp">
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\begin{equation}D\left(\vec{x},\vec{k},\omega\right)=i\sigma\Gamma_{0}+\Gamma_{1}+\vec{n}_{\perp}\cdot\vec{n}_{\perp}\frac{P\omega}{\omega_{ce}}\left(1+\zeta Z\left(\zeta\right)\right)\left(\Gamma_{2} + \Gamma_{5}F\right)\equiv 0 \end{equation}
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</p>
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<h1><a class="anchor" id="absorption_model_root"></a>
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Root Find</h1>
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<p>One way to solve for the imaginary component is to locate the root of the hot plasma dispersion function using the cold plasma solution as an intial quess. We start by redefining \(\vec{k}=k_{amp}\hat{k}\) now we can solve for the complex value of \(k_{amp}\) using a <a class="el" href="namespacesolver.html#a9ea33ed41cdc7b896ecd6004eb5b36e4">Newton method</a>.</p>
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<p>One way to solve for the imaginary component is to locate the root of the hot plasma dispersion function using the cold plasma solution as an initial guess. We start by redefining \(\vec{k}=k_{amp}\hat{k}\) now we can solve for the complex value of \(k_{amp}\) using a <a class="el" href="namespacesolver.html#af0236e2736c071193fed379d294cc437">Newton method</a>.</p>
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<hr />
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<h1><a class="anchor" id="absorption_model_damping"></a>
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Weak Damping</h1>
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<div class="line"> <span class="keywordtype">void</span> <a class="code hl_function" href="jit__test_8cpp.html#aba42e711f177787a48d91849e3ffcb09">compile</a>() {</div>
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<div class="line"> <span class="keywordtype">void</span> <a class="code hl_function" href="jit__test_8cpp.html#a27b34348d63e1712a46eef8cd89f8234">compile</a>() {</div>
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<div class="line"> <span class="keywordtype">void</span> run(<span class="keyword">const</span> <span class="keywordtype">size_t</span> time_index) {</div>
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<div class="line"> }</div>
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<div class="line">};</div>
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<div class="ttc" id="ajit__test_8cpp_html_aba42e711f177787a48d91849e3ffcb09"><div class="ttname"><a href="jit__test_8cpp.html#aba42e711f177787a48d91849e3ffcb09">compile</a></div><div class="ttdeci">void compile(graph::input_nodes&lt; T &gt; inputs, graph::output_nodes&lt; T &gt; outputs, graph::map_nodes&lt; T &gt; setters, const T expected, const T tolarance)</div><div class="ttdoc">Compile kernal and check the result of the output.</div><div class="ttdef"><b>Definition</b> jit_test.cpp:49</div></div>
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<div class="ttc" id="ajit__test_8cpp_html_a27b34348d63e1712a46eef8cd89f8234"><div class="ttname"><a href="jit__test_8cpp.html#a27b34348d63e1712a46eef8cd89f8234">compile</a></div><div class="ttdeci">void compile(graph::input_nodes&lt; T &gt; inputs, graph::output_nodes&lt; T &gt; outputs, graph::map_nodes&lt; T &gt; setters, const T expected, const T tolerance)</div><div class="ttdoc">Compile kernal and check the result of the output.</div><div class="ttdef"><b>Definition</b> jit_test.cpp:49</div></div>
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<div class="ttc" id="anamespaceequilibrium_html_a9f4ba1563110e2443131808c94663444"><div class="ttname"><a href="namespaceequilibrium.html#a9f4ba1563110e2443131808c94663444">equilibrium::shared</a></div><div class="ttdeci">std::shared_ptr&lt; generic&lt; T, SAFE_MATH &gt; &gt; shared</div><div class="ttdoc">Convenience type alias for shared equilibria.</div><div class="ttdef"><b>Definition</b> equilibrium.hpp:472</div></div>
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<div class="ttc" id="anamespacegraph_html_ac8853b055dcbbfd35dff9b4584d5ef36"><div class="ttname"><a href="namespacegraph.html#ac8853b055dcbbfd35dff9b4584d5ef36">graph::shared_leaf</a></div><div class="ttdeci">std::shared_ptr&lt; leaf_node&lt; T, SAFE_MATH &gt; &gt; shared_leaf</div><div class="ttdoc">Convenience type alias for shared leaf nodes.</div><div class="ttdef"><b>Definition</b> node.hpp:673</div></div>
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<div class="ttc" id="anamespacegraph_html_ac8853b055dcbbfd35dff9b4584d5ef36"><div class="ttname"><a href="namespacegraph.html#ac8853b055dcbbfd35dff9b4584d5ef36">graph::shared_leaf</a></div><div class="ttdeci">std::shared_ptr&lt; leaf_node&lt; T, SAFE_MATH &gt; &gt; shared_leaf</div><div class="ttdoc">Convenience type alias for shared leaf nodes.</div><div class="ttdef"><b>Definition</b> node.hpp:674</div></div>
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