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{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-17T13:05:35","documenter_version":"1.7.0"}}
{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-10-17T13:11:13","documenter_version":"1.7.0"}}
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)
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integrand(op::SingleLayerTrace, kernel, g, τ, f, σ) = f[1]*g[1]*kernel.green</code></pre><p>Every kernel corresponds with a type. Kernels can potentially depend on a set of parameters; these appear as fields in the type. Here our Nitsche kernel depends on the wavenumber. In quaddata we precompute quadrature points for all geometric cells in the supports of test and trial elements. This is fairly sloppy: only one rule for test and trial integration is considered. A high accuracy implementation would typically compute points for both low quality and high quality quadrature rules.</p><p>Also <code>quadrule</code> is sloppy: we always select a <code>DoubleQuadRule</code> to perform the computation of interactions between local shape functions. No singularity extraction or other advanced technique is considered for nearby interactions. Clearly amateurs at work here!</p><p><code>BEAST</code> provides a default implementation of an integration routine using double numerical quadrature. All that is required to tap into that implementation is a method overloading <code>integrand</code>. From the above formula it is clear what this method should look like.</p><p>That&#39;s it!</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« BEAST.jl documentation</a><a class="docs-footer-nextpage" href="../assets/postproc/">Post-processing and Visualisation »</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 1.7.0 on <span class="colophon-date" title="Thursday 17 October 2024 13:05">Thursday 17 October 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
integrand(op::SingleLayerTrace, kernel, g, τ, f, σ) = f[1]*g[1]*kernel.green</code></pre><p>Every kernel corresponds with a type. Kernels can potentially depend on a set of parameters; these appear as fields in the type. Here our Nitsche kernel depends on the wavenumber. In quaddata we precompute quadrature points for all geometric cells in the supports of test and trial elements. This is fairly sloppy: only one rule for test and trial integration is considered. A high accuracy implementation would typically compute points for both low quality and high quality quadrature rules.</p><p>Also <code>quadrule</code> is sloppy: we always select a <code>DoubleQuadRule</code> to perform the computation of interactions between local shape functions. No singularity extraction or other advanced technique is considered for nearby interactions. Clearly amateurs at work here!</p><p><code>BEAST</code> provides a default implementation of an integration routine using double numerical quadrature. All that is required to tap into that implementation is a method overloading <code>integrand</code>. From the above formula it is clear what this method should look like.</p><p>That&#39;s it!</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« BEAST.jl documentation</a><a class="docs-footer-nextpage" href="../assets/postproc/">Post-processing and Visualisation »</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 1.7.0 on <span class="colophon-date" title="Thursday 17 October 2024 13:11">Thursday 17 October 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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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Post-processing and Visualisation · BEAST Documentation</title><meta name="title" content="Post-processing and Visualisation · BEAST Documentation"/><meta property="og:title" content="Post-processing and Visualisation · BEAST Documentation"/><meta property="twitter:title" content="Post-processing and Visualisation · BEAST Documentation"/><meta name="description" content="Documentation for BEAST Documentation."/><meta property="og:description" content="Documentation for BEAST Documentation."/><meta property="twitter:description" content="Documentation for BEAST Documentation."/><script data-outdated-warner src="../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" 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href="../themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">BEAST Documentation</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><a class="tocitem" href="../../">BEAST.jl documentation</a></li><li><a class="tocitem" href="../../assemble/">The Matrix Assemble Routine</a></li><li class="is-active"><a class="tocitem" href>Post-processing and Visualisation</a><ul class="internal"><li><a class="tocitem" href="#Field-computation"><span>Field computation</span></a></li></ul></li><li><a class="tocitem" href="../../quadstrat/">Quadrature strategies</a></li><li><a class="tocitem" href="../../tdefie/">Solving the Time Domain EFIE using Marching-on-in-Time</a></li><li><a class="tocitem" href="../../tutorial/">Tutorial</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 class="is-active"><a href>Post-processing and Visualisation</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Post-processing and Visualisation</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/krcools/BEAST.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/krcools/BEAST.jl/blob/master/docs/src/assets/postproc.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="Post-processing-and-Visualisation"><a class="docs-heading-anchor" href="#Post-processing-and-Visualisation">Post-processing and Visualisation</a><a id="Post-processing-and-Visualisation-1"></a><a class="docs-heading-anchor-permalink" href="#Post-processing-and-Visualisation" title="Permalink"></a></h1><h2 id="Field-computation"><a class="docs-heading-anchor" href="#Field-computation">Field computation</a><a id="Field-computation-1"></a><a class="docs-heading-anchor-permalink" href="#Field-computation" title="Permalink"></a></h2><p>The main API for the computation of fields in a vector of points is the potential function. This function is capable of computing</p><p class="math-container">\[F(x) = \int_{\Gamma} K(x,y) u(y) dy\]</p><p>with <span>$u(y) = \Sigma_{i=1}^N u_i f_i(y)$</span> and <span>$K(x,y)$</span> the integation kernel defining the type of potential. For example, the far field for a vector valued surface density is</p><p class="math-container">\[F(x) = \int_{\Gamma} e^{ik \frac{x \cdot y}{|x|}} u(y) dy\]</p><p>For a far field potential such as this, the value only depends on the direction, not the magnitude, of <span>$x$</span>, as can be read off from the normalisation in the exponent.</p><p>The following script computes the far field along a semi-circle in the xz-plane.</p><pre><code class="language-julia hljs">Θ, Φ = range(0.0,stop=2π,length=100), 0.0
dirs = [point(cos(ϕ)*sin(θ), sin(ϕ)*sin(θ), cos(θ)) for θ in Θ for ϕ in Φ]
farfield = potential(MWFarField3D(wavenumber=κ), dirs, u, X)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../assemble/">« The Matrix Assemble Routine</a><a class="docs-footer-nextpage" href="../../quadstrat/">Quadrature strategies »</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 1.7.0 on <span class="colophon-date" title="Thursday 17 October 2024 13:05">Thursday 17 October 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
farfield = potential(MWFarField3D(wavenumber=κ), dirs, u, X)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../assemble/">« The Matrix Assemble Routine</a><a class="docs-footer-nextpage" href="../../quadstrat/">Quadrature strategies »</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 1.7.0 on <span class="colophon-date" title="Thursday 17 October 2024 13:11">Thursday 17 October 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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function momintegrals(op, tel, bel, qr::HighPrecisionQR)
...
end</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../assets/postproc/">« Post-processing and Visualisation</a><a class="docs-footer-nextpage" href="../tdefie/">Solving the Time Domain EFIE using Marching-on-in-Time »</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 1.7.0 on <span class="colophon-date" title="Thursday 17 October 2024 13:05">Thursday 17 October 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="../assets/postproc/">« Post-processing and Visualisation</a><a class="docs-footer-nextpage" href="../tdefie/">Solving the Time Domain EFIE using Marching-on-in-Time »</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 1.7.0 on <span class="colophon-date" title="Thursday 17 October 2024 13:11">Thursday 17 October 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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