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LaTex corrections in RHS
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docs/_b_s_s_n_evolution_chi_8hpp.html

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</div><!--header-->
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<div class="contents">
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<p>RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i)\).
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<p>RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \frac{2}{3}\chi(\alpha K-\partial_i\beta^i)\).
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include &quot;<a class="el" href="_b_s_s_n_grid_so_a_8hpp_source.html">../Fields/BSSNGridSoA.hpp</a>&quot;</code><br />
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<code>#include &quot;<a class="el" href="_grid_layout_8hpp_source.html">Tensorium_Grid/Grid/GridLayout.hpp</a>&quot;</code><br />
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<tr class="memdesc:a63018070ef162fcb1bc235bd8e212f8f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Fill the RHS buffer for \(\chi\) inside the padded interior region. <br /></td></tr>
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</table>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i)\). </p>
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<div class="textblock"><p>RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \frac{2}{3}\chi(\alpha K-\partial_i\beta^i)\). </p>
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<p>The implementation evaluates </p><p class="formulaDsp">
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\[\partial_t\chi = \beta^i\partial_i\chi + \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i) + \mathcal{D}_6[\chi]
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\]

docs/dir_73f1d5e07bd4a55778447360a5071440.html

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<tr class="memitem:BSSNEvolutionATilde_2Ehpp" id="r_BSSNEvolutionATilde_2Ehpp"><td class="memItemLeft"><a href="_b_s_s_n_evolution_a_tilde_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a>&#160;</td><td class="memItemRight"><a class="el" href="_b_s_s_n_evolution_a_tilde_8hpp.html">BSSNEvolutionATilde.hpp</a></td></tr>
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<tr class="memdesc:_b_s_s_n_evolution_a_tilde_8hpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">RHS for the trace-free extrinsic curvature \(\tilde{A}_{ij}\). <br /></td></tr>
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<tr class="memitem:BSSNEvolutionChi_2Ehpp" id="r_BSSNEvolutionChi_2Ehpp"><td class="memItemLeft"><a href="_b_s_s_n_evolution_chi_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a>&#160;</td><td class="memItemRight"><a class="el" href="_b_s_s_n_evolution_chi_8hpp.html">BSSNEvolutionChi.hpp</a></td></tr>
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<tr class="memdesc:_b_s_s_n_evolution_chi_8hpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i)\). <br /></td></tr>
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<tr class="memdesc:_b_s_s_n_evolution_chi_8hpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \frac{2}{3}\chi(\alpha K-\partial_i\beta^i)\). <br /></td></tr>
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<tr class="memitem:BSSNEvolutionCommon_2Ehpp" id="r_BSSNEvolutionCommon_2Ehpp"><td class="memItemLeft"><a href="_b_s_s_n_evolution_common_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a>&#160;</td><td class="memItemRight"><a class="el" href="_b_s_s_n_evolution_common_8hpp.html">BSSNEvolutionCommon.hpp</a></td></tr>
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<tr class="memdesc:_b_s_s_n_evolution_common_8hpp"><td class="mdescLeft">&#160;</td><td class="mdescRight">Shared utilities (interior clamping helpers) for all RHS kernels. <br /></td></tr>
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<tr class="memitem:BSSNEvolutionGamma_2Ehpp" id="r_BSSNEvolutionGamma_2Ehpp"><td class="memItemLeft"><a href="_b_s_s_n_evolution_gamma_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a>&#160;</td><td class="memItemRight"><a class="el" href="_b_s_s_n_evolution_gamma_8hpp.html">BSSNEvolutionGamma.hpp</a></td></tr>

docs/files.html

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<tr id="row_0_0_3_0_1_1_0_" class="odd" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_grid_derivatives_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_grid_derivatives_8hpp.html" target="_self">BSSNGridDerivatives.hpp</a></td><td class="desc">High-order finite-difference stencils and dissipation operators used by the BSSN grid </td></tr>
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<tr id="row_0_0_3_0_1_2_" class="odd"><td class="entry"><span style="width:80px;display:inline-block;">&#160;</span><span id="arr_0_0_3_0_1_2_" class="arrow" onclick="dynsection.toggleFolder('0_0_3_0_1_2_')"><span class="arrowhead closed"></span></span><span id="img_0_0_3_0_1_2_" class="iconfolder" onclick="dynsection.toggleFolder('0_0_3_0_1_2_')"><div class="folder-icon"></div></span><a class="el" href="dir_73f1d5e07bd4a55778447360a5071440.html" target="_self">Evolution</a></td><td class="desc"></td></tr>
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<tr id="row_0_0_3_0_1_2_0_" class="even" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_evolution_a_tilde_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_evolution_a_tilde_8hpp.html" target="_self">BSSNEvolutionATilde.hpp</a></td><td class="desc">RHS for the trace-free extrinsic curvature \(\tilde{A}_{ij}\) </td></tr>
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<tr id="row_0_0_3_0_1_2_1_" class="even" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_evolution_chi_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_evolution_chi_8hpp.html" target="_self">BSSNEvolutionChi.hpp</a></td><td class="desc">RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i)\) </td></tr>
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<tr id="row_0_0_3_0_1_2_1_" class="even" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_evolution_chi_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_evolution_chi_8hpp.html" target="_self">BSSNEvolutionChi.hpp</a></td><td class="desc">RHS for the conformal factor equation \((\partial_t-\mathcal{L}_\beta)\chi = \frac{2}{3}\chi(\alpha K-\partial_i\beta^i)\) </td></tr>
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<tr id="row_0_0_3_0_1_2_2_" class="even" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_evolution_common_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_evolution_common_8hpp.html" target="_self">BSSNEvolutionCommon.hpp</a></td><td class="desc">Shared utilities (interior clamping helpers) for all RHS kernels </td></tr>
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<tr id="row_0_0_3_0_1_2_3_" class="even" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_evolution_gamma_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_evolution_gamma_8hpp.html" target="_self">BSSNEvolutionGamma.hpp</a></td><td class="desc">RHS for the contracted connection \(\tilde{\Gamma}^i\) </td></tr>
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<tr id="row_0_0_3_0_1_2_4_" class="even" style="display:none;"><td class="entry"><span style="width:112px;display:inline-block;">&#160;</span><a href="_b_s_s_n_evolution_gamma_tilde_8hpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="_b_s_s_n_evolution_gamma_tilde_8hpp.html" target="_self">BSSNEvolutionGammaTilde.hpp</a></td><td class="desc">RHS for the conformal metric \(\tilde{\gamma}_{ij}\) </td></tr>

includes/Tensorium/Physics/DiffGeometry/BSSN_Grid/Evolution/BSSNEvolutionChi.hpp

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/**
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* @file BSSNEvolutionChi.hpp
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* @brief RHS for the conformal factor equation \f$(\partial_t-\mathcal{L}_\beta)\chi = \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i)\f$.
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* @brief RHS for the conformal factor equation \f$(\partial_t-\mathcal{L}_\beta)\chi = \frac{2}{3}\chi(\alpha K-\partial_i\beta^i)\f$.
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* @details The implementation evaluates
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* \f[
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* \partial_t\chi = \beta^i\partial_i\chi + \tfrac{2}{3}\chi(\alpha K-\partial_i\beta^i) + \mathcal{D}_6[\chi]

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