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{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-09-01T02:53:53","documenter_version":"1.6.0"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2024-09-02T19:44:22","documenter_version":"1.6.0"}}
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Public API · MeshIntegrals.jl</title><meta name="title" content="Public API · MeshIntegrals.jl"/><meta property="og:title" content="Public API · MeshIntegrals.jl"/><meta property="twitter:title" content="Public API · MeshIntegrals.jl"/><meta name="description" content="Documentation for MeshIntegrals.jl."/><meta property="og:description" content="Documentation for MeshIntegrals.jl."/><meta property="twitter:description" content="Documentation for MeshIntegrals.jl."/><script data-outdated-warner src="../assets/warner.js"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" 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class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">MeshIntegrals.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><span class="tocitem">Home</span><ul><li><a class="tocitem" href="../">About</a></li><li><a class="tocitem" href="../supportmatrix/">Support Matrix</a></li></ul></li><li><span class="tocitem">Derivations</span><ul><li><a class="tocitem" href="../triangle/">Integrating a Triangle</a></li></ul></li><li class="is-active"><a class="tocitem" href>Public API</a><ul class="internal"><li><a class="tocitem" href="#Integrals"><span>Integrals</span></a></li><li><a class="tocitem" href="#Integration-Algorithms"><span>Integration Algorithms</span></a></li></ul></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 class="is-active"><a href>Public API</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Public API</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/mikeingold/MeshIntegrals.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/mikeingold/MeshIntegrals.jl/blob/main/docs/src/api.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="Public-API"><a class="docs-heading-anchor" href="#Public-API">Public API</a><a id="Public-API-1"></a><a class="docs-heading-anchor-permalink" href="#Public-API" title="Permalink"></a></h1><h2 id="Integrals"><a class="docs-heading-anchor" href="#Integrals">Integrals</a><a id="Integrals-1"></a><a class="docs-heading-anchor-permalink" href="#Integrals" title="Permalink"></a></h2><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="MeshIntegrals.integral" href="#MeshIntegrals.integral"><code>MeshIntegrals.integral</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">integral(f, geometry)
integral(f, geometry, algorithm)
integral(f, geometry, algorithm, FP)</code></pre><p>Numerically integrate a given function <code>f(::Point)</code> over the domain defined by a <code>geometry</code> using a particular <code>integration algorithm</code> with floating point precision of type <code>FP</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral.jl#L50-L58">source</a></section></article><h3 id="Aliases"><a class="docs-heading-anchor" href="#Aliases">Aliases</a><a id="Aliases-1"></a><a class="docs-heading-anchor-permalink" href="#Aliases" title="Permalink"></a></h3><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="MeshIntegrals.lineintegral" href="#MeshIntegrals.lineintegral"><code>MeshIntegrals.lineintegral</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">lineintegral(f, geometry)
lineintegral(f, geometry, algorithm)
lineintegral(f, geometry, algorithm, FP)</code></pre><p>Numerically integrate a given function <code>f(::Point)</code> along a line-like <code>geometry</code> using a particular <code>integration algorithm</code> with floating point precision of type <code>FP</code>.</p><p>Algorithm types available:</p><ul><li>GaussKronrod (default)</li><li>GaussLegendre</li><li>HAdaptiveCubature</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral_aliases.jl#L5-L18">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="MeshIntegrals.surfaceintegral" href="#MeshIntegrals.surfaceintegral"><code>MeshIntegrals.surfaceintegral</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">surfaceintegral(f, geometry)
surfaceintegral(f, geometry, algorithm)
surfaceintegral(f, geometry, algorithm, FP)</code></pre><p>Numerically integrate a given function <code>f(::Point)</code> along a surface <code>geometry</code> using a particular <code>integration algorithm</code> with floating point precision of type <code>FP</code>.</p><p>Algorithm types available:</p><ul><li>GaussKronrod</li><li>GaussLegendre</li><li>HAdaptiveCubature (default)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral_aliases.jl#L66-L79">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="MeshIntegrals.volumeintegral" href="#MeshIntegrals.volumeintegral"><code>MeshIntegrals.volumeintegral</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">volumeintegral(f, geometry)
volumeintegral(f, geometry, algorithm)
volumeintegral(f, geometry, algorithm, FP)</code></pre><p>Numerically integrate a given function <code>f(::Point)</code> throughout a volumetric <code>geometry</code> using a particular <code>integration algorithm</code> with floating point precision of type <code>FP</code>.</p><p>Algorithm types available:</p><ul><li>GaussKronrod</li><li>GaussLegendre</li><li>HAdaptiveCubature (default)</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral_aliases.jl#L127-L140">source</a></section></article><h2 id="Integration-Algorithms"><a class="docs-heading-anchor" href="#Integration-Algorithms">Integration Algorithms</a><a id="Integration-Algorithms-1"></a><a class="docs-heading-anchor-permalink" href="#Integration-Algorithms" title="Permalink"></a></h2><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="MeshIntegrals.GaussKronrod" href="#MeshIntegrals.GaussKronrod"><code>MeshIntegrals.GaussKronrod</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">GaussKronrod(kwargs...)</code></pre><p>Numerically integrate using the h-adaptive Gauss-Kronrod quadrature rule implemented by QuadGK.jl. All standard <code>QuadGK.quadgk</code> keyword arguments are supported.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral.jl#L7-L12">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="MeshIntegrals.GaussLegendre" href="#MeshIntegrals.GaussLegendre"><code>MeshIntegrals.GaussLegendre</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">GaussLegendre(n)</code></pre><p>Numerically integrate using an <code>n</code>&#39;th-order Gauss-Legendre quadrature rule. nodes and weights are efficiently calculated using FastGaussQuadrature.jl.</p><p>So long as the integrand function can be well-approximated by a polynomial of order <code>2n-1</code>, this method should yield results with 16-digit accuracy in <code>O(n)</code> time. If the function is know to have some periodic content, then <code>n</code> should (at a minimum) be greater than the expected number of periods over the geometry, e.g. <code>length(geometry)/lambda</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral.jl#L18-L29">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="MeshIntegrals.HAdaptiveCubature" href="#MeshIntegrals.HAdaptiveCubature"><code>MeshIntegrals.HAdaptiveCubature</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">GaussKronrod(kwargs...)</code></pre><p>Numerically integrate areas and surfaces using the h-adaptive cubature rule implemented by HCubature.jl. All standard <code>HCubature.hcubature</code> keyword arguments are supported.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/mikeingold/MeshIntegrals.jl/blob/d0248d3fdadf245d5a50f0732ba37d40d52fab45/src/integral.jl#L34-L40">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../triangle/">« Integrating a Triangle</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 1.6.0 on <span class="colophon-date" title="Monday 2 September 2024 19:44">Monday 2 September 2024</span>. 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