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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Hamiltonian splitting · GEMPIC</title><meta name="title" content="Hamiltonian splitting · GEMPIC"/><meta property="og:title" content="Hamiltonian splitting · GEMPIC"/><meta property="twitter:title" content="Hamiltonian splitting · GEMPIC"/><meta name="description" content="Documentation for GEMPIC."/><meta property="og:description" content="Documentation for GEMPIC."/><meta property="twitter:description" content="Documentation for GEMPIC."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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class="tocitem">Documentation</span><ul><li><a class="tocitem" href="../">GEMPIC.jl Documentation</a></li><li><a class="tocitem" href="../mesh/">Mesh</a></li><li><a class="tocitem" href="../low_level_bsplines/">Splines</a></li><li><a class="tocitem" href="../splinepp/">Periodic spline</a></li><li><a class="tocitem" href="../particle_mesh_coupling/">Particle-Mesh coupling</a></li><li><a class="tocitem" href="../distributions/">Distributions</a></li><li><a class="tocitem" href="../particle_group/">Particle group</a></li><li><a class="tocitem" href="../particle_sampling/">Particle sampling</a></li><li><a class="tocitem" href="../maxwell_solver/">Maxwell solver</a></li><li><input class="collapse-toggle" id="menuitem-1-10" type="checkbox" checked/><label class="tocitem" for="menuitem-1-10"><span class="docs-label">Splitting</span><i class="docs-chevron"></i></label><ul class="collapsed"><li class="is-active"><a class="tocitem" href>Hamiltonian splitting</a></li><li><a class="tocitem" href="../hamiltonian_splitting_boris/">Hamiltonian splitting Boris</a></li></ul></li><li><a class="tocitem" href="../diagnostics/">Diagnostics</a></li></ul></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../strong_landau_damping/">Strong Landau Damping</a></li></ul></li><li><a class="tocitem" href="../contents/">Contents</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Documentation</a></li><li><a class="is-disabled">Splitting</a></li><li class="is-active"><a href>Hamiltonian splitting</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Hamiltonian splitting</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaVlasov/GEMPIC.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/master/docs/src/hamiltonian_splitting.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Hamiltonian-splitting"><a class="docs-heading-anchor" href="#Hamiltonian-splitting">Hamiltonian splitting</a><a id="Hamiltonian-splitting-1"></a><a class="docs-heading-anchor-permalink" href="#Hamiltonian-splitting" title="Permalink"></a></h1><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="GEMPIC.HamiltonianSplitting" href="#GEMPIC.HamiltonianSplitting"><code>GEMPIC.HamiltonianSplitting</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">HamiltonianSplitting( maxwell_solver, | ||
| kernel_smoother_0, kernel_smoother_1, | ||
| particle_group, e_dofs, b_dofs)</code></pre><p>Hamiltonian splitting type for Vlasov-Maxwell</p><ul><li>Integral over the spline function on each interval (order p+1)</li><li>Integral over the spline function on each interval (order p)</li><li><code>e_dofs</code> describing the two components of the electric field</li><li><code>b_dofs</code> describing the magnetic field</li><li><code>j_dofs</code> for kernel representation of current density. </li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/27d3204f7d3fbce7dbb99c9b4b4337923d1101fb/src/hamiltonian_splitting.jl#L7-L19">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="GEMPIC.lie_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}" href="#GEMPIC.lie_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}"><code>GEMPIC.lie_splitting!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">lie_splitting( h, dt, number_steps)</code></pre><p>Lie splitting</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/27d3204f7d3fbce7dbb99c9b4b4337923d1101fb/src/hamiltonian_splitting.jl#L115-L119">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="GEMPIC.lie_splitting_back!-Tuple{HamiltonianSplitting, Float64, Int64}" href="#GEMPIC.lie_splitting_back!-Tuple{HamiltonianSplitting, Float64, Int64}"><code>GEMPIC.lie_splitting_back!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">lie_splitting_back(h, dt, number_steps)</code></pre><p>Lie splitting (oposite ordering)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/27d3204f7d3fbce7dbb99c9b4b4337923d1101fb/src/hamiltonian_splitting.jl#L130-L134">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="GEMPIC.strang_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}" href="#GEMPIC.strang_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}"><code>GEMPIC.strang_splitting!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">strang_splitting( h, dt, number_steps)</code></pre><p>Strang splitting</p><ul><li>time splitting object </li><li>time step</li><li>number of time steps</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/27d3204f7d3fbce7dbb99c9b4b4337923d1101fb/src/hamiltonian_splitting.jl#L94-L101">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../maxwell_solver/">« Maxwell solver</a><a class="docs-footer-nextpage" href="../hamiltonian_splitting_boris/">Hamiltonian splitting Boris »</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 1.5.0 on <span class="colophon-date" title="Monday 22 July 2024 13:05">Monday 22 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> | ||
| particle_group, e_dofs, b_dofs)</code></pre><p>Hamiltonian splitting type for Vlasov-Maxwell</p><ul><li>Integral over the spline function on each interval (order p+1)</li><li>Integral over the spline function on each interval (order p)</li><li><code>e_dofs</code> describing the two components of the electric field</li><li><code>b_dofs</code> describing the magnetic field</li><li><code>j_dofs</code> for kernel representation of current density. </li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/16d82d4a28cd8fd1998d77fe2032d63562f2fe28/src/hamiltonian_splitting.jl#L7-L19">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="GEMPIC.lie_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}" href="#GEMPIC.lie_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}"><code>GEMPIC.lie_splitting!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">lie_splitting( h, dt, number_steps)</code></pre><p>Lie splitting</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/16d82d4a28cd8fd1998d77fe2032d63562f2fe28/src/hamiltonian_splitting.jl#L115-L119">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="GEMPIC.lie_splitting_back!-Tuple{HamiltonianSplitting, Float64, Int64}" href="#GEMPIC.lie_splitting_back!-Tuple{HamiltonianSplitting, Float64, Int64}"><code>GEMPIC.lie_splitting_back!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">lie_splitting_back(h, dt, number_steps)</code></pre><p>Lie splitting (oposite ordering)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/16d82d4a28cd8fd1998d77fe2032d63562f2fe28/src/hamiltonian_splitting.jl#L130-L134">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="GEMPIC.strang_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}" href="#GEMPIC.strang_splitting!-Tuple{HamiltonianSplitting, Float64, Int64}"><code>GEMPIC.strang_splitting!</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">strang_splitting( h, dt, number_steps)</code></pre><p>Strang splitting</p><ul><li>time splitting object </li><li>time step</li><li>number of time steps</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaVlasov/GEMPIC.jl/blob/16d82d4a28cd8fd1998d77fe2032d63562f2fe28/src/hamiltonian_splitting.jl#L94-L101">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../maxwell_solver/">« Maxwell solver</a><a class="docs-footer-nextpage" href="../hamiltonian_splitting_boris/">Hamiltonian splitting Boris »</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 1.5.0 on <span class="colophon-date" title="Monday 22 July 2024 13:05">Monday 22 July 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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