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{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-24T10:34:44","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-24T10:35:31","documenter_version":"1.8.0"}}
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pvd[t] = vtm # save to pvd!
end
end
end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../implicit_utils/">« Functionalities for implicit methods</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:34">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../implicit_utils/">« Functionalities for implicit methods</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:35">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/generation/index.html
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[0.0 0.0; 0.0 0.0]
[0.0 0.0; 0.0 0.0]
[0.0 0.0; 0.0 0.0]
[0.0 0.0; 0.0 0.0]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/particles.jl#L54-L107">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Tesserae.GridSampling" href="#Tesserae.GridSampling"><code>Tesserae.GridSampling</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">GridSampling(spacing = 1/2)</code></pre><p>The generated particles are aligned with the grid using uniform spacing. Setting <code>spacing = 1/η</code> will produce <code>η^dim</code> particles per cell, where <code>dim</code> is the problem dimension.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/particles.jl#L3-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Tesserae.PoissonDiskSampling" href="#Tesserae.PoissonDiskSampling"><code>Tesserae.PoissonDiskSampling</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PoissonDiskSampling(spacing = 1/2, rng = Random.default_rng())</code></pre><p>The particles are generated based on the Poisson disk sampling. The <code>spacing</code> parameter is used to produce a similar number of particles as are generated with <a href="#Tesserae.GridSampling"><code>GridSampling</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/particles.jl#L19-L24">source</a></section></article><p><img src="https://github.com/user-attachments/assets/1ed7db73-cce2-47b2-84fc-9e895b9a89a7" alt/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../mesh/">« Mesh</a><a class="docs-footer-nextpage" href="../interpolation/">Interpolation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:34">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
[0.0 0.0; 0.0 0.0]</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/particles.jl#L54-L107">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Tesserae.GridSampling" href="#Tesserae.GridSampling"><code>Tesserae.GridSampling</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">GridSampling(spacing = 1/2)</code></pre><p>The generated particles are aligned with the grid using uniform spacing. Setting <code>spacing = 1/η</code> will produce <code>η^dim</code> particles per cell, where <code>dim</code> is the problem dimension.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/particles.jl#L3-L8">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Tesserae.PoissonDiskSampling" href="#Tesserae.PoissonDiskSampling"><code>Tesserae.PoissonDiskSampling</code></a><span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">PoissonDiskSampling(spacing = 1/2, rng = Random.default_rng())</code></pre><p>The particles are generated based on the Poisson disk sampling. The <code>spacing</code> parameter is used to produce a similar number of particles as are generated with <a href="#Tesserae.GridSampling"><code>GridSampling</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/particles.jl#L19-L24">source</a></section></article><p><img src="https://github.com/user-attachments/assets/1ed7db73-cce2-47b2-84fc-9e895b9a89a7" alt/></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../mesh/">« Mesh</a><a class="docs-footer-nextpage" href="../interpolation/">Interpolation »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:35">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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= \frac{\partial w}{\partial X_i} \frac{\partial X_i}{\partial x_j}
= \frac{\partial w}{\partial X_i} \Delta{F}_{ij}^{-1}\]</p><p>where</p><p class="math-container">\[\Delta{F}_{ij}
= \frac{\partial x_i}{\partial X_j}
= \delta_{ij} + \frac{\partial u_i}{\partial X_j}.\]</p><p>This relative deformation gradient <span>$\Delta\bm{F}$</span> is typically used to update the deformation gradient in MPM:</p><p class="math-container">\[F_{ij} = \Delta{F}_{ik} F_{kj}^n.\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorials/tlmpm_vortex/">« Total Lagrangian MPM</a><a class="docs-footer-nextpage" href="../tutorials/implicit_jacobian_free/">Jacobian-free »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:34">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
= \delta_{ij} + \frac{\partial u_i}{\partial X_j}.\]</p><p>This relative deformation gradient <span>$\Delta\bm{F}$</span> is typically used to update the deformation gradient in MPM:</p><p class="math-container">\[F_{ij} = \Delta{F}_{ik} F_{kj}^n.\]</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../tutorials/tlmpm_vortex/">« Total Lagrangian MPM</a><a class="docs-footer-nextpage" href="../tutorials/implicit_jacobian_free/">Jacobian-free »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:35">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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true

julia&gt; x ≈ [0,1]
true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/implicit.jl#L337-L367">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../transfer/">« Transfer between grid and particles</a><a class="docs-footer-nextpage" href="../export/">Export »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:34">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/KeitaNakamura/Tesserae.jl/blob/577a706dc40684f3c13f72ccde1a13390a822d79/src/implicit.jl#L337-L367">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../transfer/">« Transfer between grid and particles</a><a class="docs-footer-nextpage" href="../export/">Export »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 24 November 2024 10:35">Sunday 24 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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