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<p>Nodal tyings per periodic boundary conditions.
<a href="#details">More...</a></p>
<p><code>#include &lt;<a class="el" href="TyingsPeriodic_8h_source.html">GooseFEM/TyingsPeriodic.h</a>&gt;</code></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="pub-methods" name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a13b3ccb84480dce4eabff664003ec420" id="r_a13b3ccb84480dce4eabff664003ec420"><td class="memTemplParams" colspan="2">template&lt;<a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">C</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">D</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">S</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">T</a> &gt; </td></tr>
<tr class="memitem:a13b3ccb84480dce4eabff664003ec420"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a13b3ccb84480dce4eabff664003ec420">Periodic</a> (<a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">C</a> &amp;coor, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">D</a> &amp;<a class="el" href="#a9cc18047ef3f0262beef32234d8fe2d9">dofs</a>, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">S</a> &amp;<a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">control_dofs</a>, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">T</a> &amp;<a class="el" href="#af7aeffaf99596b6265db5178d517f958">nodal_tyings</a>)</td></tr>
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<tr class="memitem:a2a16eba1fa229975c206105e56e2d672" id="r_a2a16eba1fa229975c206105e56e2d672"><td class="memTemplParams" colspan="2">template&lt;<a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">C</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">D</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">S</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">T</a> , <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">class</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">U</a> &gt; </td></tr>
<tr class="memitem:a2a16eba1fa229975c206105e56e2d672"><td class="memTemplItemLeft" align="right" valign="top">&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="#a2a16eba1fa229975c206105e56e2d672">Periodic</a> (<a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">C</a> &amp;coor, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">D</a> &amp;<a class="el" href="#a9cc18047ef3f0262beef32234d8fe2d9">dofs</a>, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">S</a> &amp;<a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">control_dofs</a>, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">T</a> &amp;<a class="el" href="#af7aeffaf99596b6265db5178d517f958">nodal_tyings</a>, <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">U</a> &amp;<a class="el" href="#a4985863027dfda9e9d939bbf87ef4232">iip</a>)</td></tr>
<tr class="memdesc:a2a16eba1fa229975c206105e56e2d672"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor. <br /></td></tr>
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<tr class="memitem:ac1ffeefa729122e3fbeafc806b1527e3" id="r_ac1ffeefa729122e3fbeafc806b1527e3"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ac1ffeefa729122e3fbeafc806b1527e3">nnd</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
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<tr class="memitem:ab6ee785b1d6c2fdcbe8fa2c71d380bf0" id="r_ab6ee785b1d6c2fdcbe8fa2c71d380bf0"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ab6ee785b1d6c2fdcbe8fa2c71d380bf0">nni</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
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<tr class="memitem:a03a090236d964de2b288cda9036710d4" id="r_a03a090236d964de2b288cda9036710d4"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a03a090236d964de2b288cda9036710d4">nnu</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
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<tr class="memitem:a4b1acf54dc71e271c717c510c2b593a7" id="r_a4b1acf54dc71e271c717c510c2b593a7"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a4b1acf54dc71e271c717c510c2b593a7">nnp</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
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<tr class="memitem:a9cc18047ef3f0262beef32234d8fe2d9" id="r_a9cc18047ef3f0262beef32234d8fe2d9"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 2 &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a9cc18047ef3f0262beef32234d8fe2d9">dofs</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="separator:a9cc18047ef3f0262beef32234d8fe2d9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab50f4a483af8a5475db95af4cffff663" id="r_ab50f4a483af8a5475db95af4cffff663"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 2 &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ab50f4a483af8a5475db95af4cffff663">control</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
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<tr class="memitem:af7aeffaf99596b6265db5178d517f958" id="r_af7aeffaf99596b6265db5178d517f958"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 2 &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af7aeffaf99596b6265db5178d517f958">nodal_tyings</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:af7aeffaf99596b6265db5178d517f958"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return the applied nodal tyings. <br /></td></tr>
<tr class="separator:af7aeffaf99596b6265db5178d517f958"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7f108d7716a1e2f8e96c73cea74ae78b" id="r_a7f108d7716a1e2f8e96c73cea74ae78b"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a7f108d7716a1e2f8e96c73cea74ae78b">iid</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:a7f108d7716a1e2f8e96c73cea74ae78b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Dependent DOFs. <br /></td></tr>
<tr class="separator:a7f108d7716a1e2f8e96c73cea74ae78b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a94917fec18c3d524b4317d37a730cc1d" id="r_a94917fec18c3d524b4317d37a730cc1d"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a94917fec18c3d524b4317d37a730cc1d">iii</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:a94917fec18c3d524b4317d37a730cc1d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Independent DOFs. <br /></td></tr>
<tr class="separator:a94917fec18c3d524b4317d37a730cc1d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6ff7cbd5136d3cfede8d4464dfb9b0b6" id="r_a6ff7cbd5136d3cfede8d4464dfb9b0b6"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a6ff7cbd5136d3cfede8d4464dfb9b0b6">iiu</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:a6ff7cbd5136d3cfede8d4464dfb9b0b6"><td class="mdescLeft">&#160;</td><td class="mdescRight">Independent unknown DOFs. <br /></td></tr>
<tr class="separator:a6ff7cbd5136d3cfede8d4464dfb9b0b6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4985863027dfda9e9d939bbf87ef4232" id="r_a4985863027dfda9e9d939bbf87ef4232"><td class="memItemLeft" align="right" valign="top"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a4985863027dfda9e9d939bbf87ef4232">iip</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:a4985863027dfda9e9d939bbf87ef4232"><td class="mdescLeft">&#160;</td><td class="mdescRight">Independent prescribed DOFs. <br /></td></tr>
<tr class="separator:a4985863027dfda9e9d939bbf87ef4232"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ada07b0607da8c5cb75ecf61cdba4e7e8" id="r_ada07b0607da8c5cb75ecf61cdba4e7e8"><td class="memItemLeft" align="right" valign="top">Eigen::SparseMatrix&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">double</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ada07b0607da8c5cb75ecf61cdba4e7e8">Cdi</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:ada07b0607da8c5cb75ecf61cdba4e7e8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return tying matrix such as to get the dependent DOFs \( u_d \) from the independent DOFs \( u_i \) as follows. <br /></td></tr>
<tr class="separator:ada07b0607da8c5cb75ecf61cdba4e7e8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a49356b79bbe49769bb20f385b58e4f20" id="r_a49356b79bbe49769bb20f385b58e4f20"><td class="memItemLeft" align="right" valign="top">Eigen::SparseMatrix&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">double</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a49356b79bbe49769bb20f385b58e4f20">Cdu</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:a49356b79bbe49769bb20f385b58e4f20"><td class="mdescLeft">&#160;</td><td class="mdescRight">Unknown part of the partitioned tying matrix, see <a class="el" href="#ada07b0607da8c5cb75ecf61cdba4e7e8" title="Return tying matrix such as to get the dependent DOFs from the independent DOFs as follows.">Cdi()</a>. <br /></td></tr>
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<tr class="memitem:a3d5b282025f8240f97ff5c85c3db4265" id="r_a3d5b282025f8240f97ff5c85c3db4265"><td class="memItemLeft" align="right" valign="top">Eigen::SparseMatrix&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">double</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a3d5b282025f8240f97ff5c85c3db4265">Cdp</a> () <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a></td></tr>
<tr class="memdesc:a3d5b282025f8240f97ff5c85c3db4265"><td class="mdescLeft">&#160;</td><td class="mdescRight">Prescribed part of the partitioned tying matrix, see <a class="el" href="#ada07b0607da8c5cb75ecf61cdba4e7e8" title="Return tying matrix such as to get the dependent DOFs from the independent DOFs as follows.">Cdi()</a>. <br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Nodal tyings per periodic boundary conditions. </p>
<p>The idea is that the displacement of all DOFs of a node are tied to another node and to the average displacement gradient. The latter is applied/measured using 'virtual' control nodes.</p>
<p>Consider the DOF list \( u \) renumbered such that it is split up in independent and dependent DOFs as follows</p>
<p>\( u = \begin{bmatrix} u_i \\ u_d \end{bmatrix}\)</p>
<p>whereby the independent DOFs are furthermore split up in unknown and prescribed nodes as follows</p>
<p>\( u_i = \begin{bmatrix} u_u \\ u_p \end{bmatrix}\)</p>
<p>such that</p>
<p>\( u = \begin{bmatrix} u_u \\ u_p \\ u_d \end{bmatrix}\)</p>
<dl class="todo"><dt><b><a class="el" href="todo.html#_todo000005">Todo</a></b></dt><dd>Document how the DOFs are tied to the control nodes, and what the has to do with the mean. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00046">46</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
</div><h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a13b3ccb84480dce4eabff664003ec420">&#9670;&#160;</a></span>Periodic() <span class="overload">[1/2]</span></h2>
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<td class="memname">GooseFEM::Tyings::Periodic::Periodic </td>
<td>(</td>
<td class="paramtype"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">C</a> &amp;</td> <td class="paramname"><span class="paramname"><em>coor</em>, </span></td>
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<td class="paramtype"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">D</a> &amp;</td> <td class="paramname"><span class="paramname"><em>dofs</em>, </span></td>
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<p>Constructor. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
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<tr><td class="paramname">C</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;double, 2&gt;</a> </td></tr>
<tr><td class="paramname">D</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 2&gt;</a> </td></tr>
<tr><td class="paramname">S</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 2&gt;</a> </td></tr>
<tr><td class="paramname">T</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 2&gt;</a> </td></tr>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">coor</td><td>Nodal coordinates [nnode, ndim]. </td></tr>
<tr><td class="paramname">dofs</td><td>DOF-numbers per node [nnode, ndim]. </td></tr>
<tr><td class="paramname">control_dofs</td><td>DOF-numbers per control node [ndim, ndim]. </td></tr>
<tr><td class="paramname">nodal_tyings</td><td>List of nodal tyings, see <a class="el" href="#af7aeffaf99596b6265db5178d517f958" title="Return the applied nodal tyings.">nodal_tyings()</a>. [ntyings, 2]. </td></tr>
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<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00063">63</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a2a16eba1fa229975c206105e56e2d672">&#9670;&#160;</a></span>Periodic() <span class="overload">[2/2]</span></h2>
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<td class="memname">GooseFEM::Tyings::Periodic::Periodic </td>
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<td class="paramtype"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">D</a> &amp;</td> <td class="paramname"><span class="paramname"><em>dofs</em>, </span></td>
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<td class="paramtype"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">S</a> &amp;</td> <td class="paramname"><span class="paramname"><em>control_dofs</em>, </span></td>
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<td class="paramtype"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">T</a> &amp;</td> <td class="paramname"><span class="paramname"><em>nodal_tyings</em>, </span></td>
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<p>Constructor. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
<table class="tparams">
<tr><td class="paramname">C</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;double, 2&gt;</a> </td></tr>
<tr><td class="paramname">D</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 2&gt;</a> </td></tr>
<tr><td class="paramname">S</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 2&gt;</a> </td></tr>
<tr><td class="paramname">T</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 2&gt;</a> </td></tr>
<tr><td class="paramname">U</td><td><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1" title="Fixed (static) rank array.">array_type::tensor&lt;size_t, 1&gt;</a> </td></tr>
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<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">coor</td><td>Nodal coordinates [nnode, ndim]. </td></tr>
<tr><td class="paramname">dofs</td><td>DOF-numbers per node [nnode, ndim]. </td></tr>
<tr><td class="paramname">control_dofs</td><td>DOF-numbers per control node [ndim, ndim]. </td></tr>
<tr><td class="paramname">nodal_tyings</td><td>List of nodal tyings, see <a class="el" href="#af7aeffaf99596b6265db5178d517f958" title="Return the applied nodal tyings.">nodal_tyings()</a>. [ntyings, 2]. </td></tr>
<tr><td class="paramname">iip</td><td>List of prescribed DOF-numbers. </td></tr>
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<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00083">83</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ada07b0607da8c5cb75ecf61cdba4e7e8">&#9670;&#160;</a></span>Cdi()</h2>
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<td class="memname">Eigen::SparseMatrix&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">double</a> &gt; GooseFEM::Tyings::Periodic::Cdi </td>
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<p>Return tying matrix such as to get the dependent DOFs \( u_d \) from the independent DOFs \( u_i \) as follows. </p>
<p>\( u_d = C_{di} u_i \)</p>
<p>Note that this can be further partitioned in</p>
<p>\( u_d = C_{du} u_u + C_{dp} u_p \)</p>
<p>See <a class="el" href="#a49356b79bbe49769bb20f385b58e4f20" title="Unknown part of the partitioned tying matrix, see Cdi().">Cdu()</a> and <a class="el" href="#a3d5b282025f8240f97ff5c85c3db4265" title="Prescribed part of the partitioned tying matrix, see Cdi().">Cdp()</a>.</p>
<dl class="section return"><dt>Returns</dt><dd>Sparse matrix. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00238">238</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a3d5b282025f8240f97ff5c85c3db4265">&#9670;&#160;</a></span>Cdp()</h2>
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<td class="memname">Eigen::SparseMatrix&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">double</a> &gt; GooseFEM::Tyings::Periodic::Cdp </td>
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<p>Prescribed part of the partitioned tying matrix, see <a class="el" href="#ada07b0607da8c5cb75ecf61cdba4e7e8" title="Return tying matrix such as to get the dependent DOFs from the independent DOFs as follows.">Cdi()</a>. </p>
<dl class="section return"><dt>Returns</dt><dd>Sparse matrix. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00310">310</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a49356b79bbe49769bb20f385b58e4f20">&#9670;&#160;</a></span>Cdu()</h2>
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<td class="memname">Eigen::SparseMatrix&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">double</a> &gt; GooseFEM::Tyings::Periodic::Cdu </td>
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<p>Unknown part of the partitioned tying matrix, see <a class="el" href="#ada07b0607da8c5cb75ecf61cdba4e7e8" title="Return tying matrix such as to get the dependent DOFs from the independent DOFs as follows.">Cdi()</a>. </p>
<dl class="section return"><dt>Returns</dt><dd>Sparse matrix. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00272">272</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab50f4a483af8a5475db95af4cffff663">&#9670;&#160;</a></span>control()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 2 &gt; &amp; GooseFEM::Tyings::Periodic::control </td>
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<dl class="section return"><dt>Returns</dt><dd>DOF-numbers for each control node, as used internally (after renumbering), [ndim, ndim]. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00167">167</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a9cc18047ef3f0262beef32234d8fe2d9">&#9670;&#160;</a></span>dofs()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 2 &gt; &amp; GooseFEM::Tyings::Periodic::dofs </td>
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<dl class="section return"><dt>Returns</dt><dd>DOF-numbers per node, as used internally (after renumbering), [nnode, ndim]. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00158">158</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a7f108d7716a1e2f8e96c73cea74ae78b">&#9670;&#160;</a></span>iid()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt; GooseFEM::Tyings::Periodic::iid </td>
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<p>Dependent DOFs. </p>
<dl class="section return"><dt>Returns</dt><dd>List of DOF numbers. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00189">189</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a94917fec18c3d524b4317d37a730cc1d">&#9670;&#160;</a></span>iii()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt; GooseFEM::Tyings::Periodic::iii </td>
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<p>Independent DOFs. </p>
<dl class="section return"><dt>Returns</dt><dd>List of DOF numbers. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00199">199</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4985863027dfda9e9d939bbf87ef4232">&#9670;&#160;</a></span>iip()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt; GooseFEM::Tyings::Periodic::iip </td>
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<p>Independent prescribed DOFs. </p>
<dl class="section return"><dt>Returns</dt><dd>List of DOF numbers. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00219">219</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a6ff7cbd5136d3cfede8d4464dfb9b0b6">&#9670;&#160;</a></span>iiu()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 1 &gt; GooseFEM::Tyings::Periodic::iiu </td>
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<p>Independent unknown DOFs. </p>
<dl class="section return"><dt>Returns</dt><dd>List of DOF numbers. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00209">209</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ac1ffeefa729122e3fbeafc806b1527e3">&#9670;&#160;</a></span>nnd()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a> GooseFEM::Tyings::Periodic::nnd </td>
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<dl class="section return"><dt>Returns</dt><dd>Number of dependent DOFs. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00126">126</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ab6ee785b1d6c2fdcbe8fa2c71d380bf0">&#9670;&#160;</a></span>nni()</h2>
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<dl class="section return"><dt>Returns</dt><dd>Number of independent DOFs. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00134">134</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a4b1acf54dc71e271c717c510c2b593a7">&#9670;&#160;</a></span>nnp()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a> GooseFEM::Tyings::Periodic::nnp </td>
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<dl class="section return"><dt>Returns</dt><dd>Number of independent prescribed DOFs. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00150">150</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a03a090236d964de2b288cda9036710d4">&#9670;&#160;</a></span>nnu()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a> GooseFEM::Tyings::Periodic::nnu </td>
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<dl class="section return"><dt>Returns</dt><dd>Number of independent unknown DOFs. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00142">142</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#af7aeffaf99596b6265db5178d517f958">&#9670;&#160;</a></span>nodal_tyings()</h2>
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<td class="memname"><a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">const</a> <a class="el" href="namespaceGooseFEM_1_1array__type.html#adad35bf4db4c7eb54c25136f0f3d34d1">array_type::tensor</a>&lt; <a class="el" href="namespaceGooseFEM.html#acb082fa83b6ad7cf3a04bd7a181cce81">size_t</a>, 2 &gt; &amp; GooseFEM::Tyings::Periodic::nodal_tyings </td>
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<p>Return the applied nodal tyings. </p>
<p>Per tying (row) two node numbers are specified, according to the convention (independent, dependent).</p>
<dl class="section return"><dt>Returns</dt><dd>[ntyings, 2]. </dd></dl>
<p class="definition">Definition at line <a class="el" href="TyingsPeriodic_8h_source.html#l00179">179</a> of file <a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a>.</p>
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<hr/>The documentation for this class was generated from the following file:<ul>
<li>GooseFEM/<a class="el" href="TyingsPeriodic_8h_source.html">TyingsPeriodic.h</a></li>
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