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end</code></pre><p>In the monolithic assembly of <code>MultiFieldFESpaces</code>, the variable <code>A</code> is an <code>ArrayCounter</code>. As you can see, all contribution blocks (coming from different fields) are assembled into the same <code>ArrayCounter</code>. The block-assembly counterpart will have the input <code>A</code> be a <code>MatrixBlock{&lt;:ArrayCounter}</code>, and assembles each contribution block to it&#39;s corresponding <code>ArrayCounter</code> (notice the <code>A.array[i,j]</code>).</p><h3 id="B)-Assembling-multiple-FE-Fields-into-the-same-Block"><a class="docs-heading-anchor" href="#B)-Assembling-multiple-FE-Fields-into-the-same-Block">B) Assembling multiple FE Fields into the same Block</a><a id="B)-Assembling-multiple-FE-Fields-into-the-same-Block-1"></a><a class="docs-heading-anchor-permalink" href="#B)-Assembling-multiple-FE-Fields-into-the-same-Block" title="Permalink"></a></h3><p>The <code>BlockMultiFieldStyle</code> constructor can take up to three parameters:</p><ol><li><code>NB</code> :: Integer, representing the number of final blocks. Then the matrix and vector will have <code>NBxNB</code> and <code>NB</code> blocks respectively.</li><li><code>SB</code> :: Tuple of integers, of length <code>NB</code>. In each position, <code>SB[ib]</code> is the number of fields that will be assembled in that block.</li><li><code>P</code> :: Tuple of integers, of length the number of fields. This represents a field permutation, such that the fields will be reordered as<code>[P[1],P[2],....,P[n]]</code>.</li></ol><p>Using this three parameters, one can assemble an arbitrary number of fields into any number of blocks.</p><p><strong>Example</strong>: Consider we are solving an MHD problem with variables <code>(u,p,j,q)</code> , i.e (fluid velocity, fluid pressure, magnetic current, electric potential). Although the variables are in this specific order in the <code>MultiFieldFESpace</code>, we want to build a block-preconditioner that solves <code>(u,j)</code> together in a single block then <code>p</code> and <code>q</code> separately in two other blocks. Then we would need to assemble our system using <code>NB=3</code>, <code>SB=(2,1,1)</code> and <code>P=(1,3,2,4)</code>. With this configuration, we will create 3 blocks. The first block will have size 2 and hold variables <code>[P[1],P[2]] = [1,3] = [u,j]</code>. The second block will have size 1 and hold variables <code>[P[3]] = [2] = [p]</code>. Finally, the third block will hold variables <code>[P[4]] = [4] = [q]</code>.</p><p>In terms of implementation, everything is the same. We use <code>ArrayBlockViews</code> (which is a view counterpart of <code>ArrayBlock</code>) so that an array of <code>NBxNB</code> array builders / array counters can be indexed using the field indexes. This allows us to use the same dispatches as we had in part A.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Adaptivity/">« Gridap.Adaptivity</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Monday 16 October 2023 07:18">Monday 16 October 2023</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><p>In the monolithic assembly of <code>MultiFieldFESpaces</code>, the variable <code>A</code> is an <code>ArrayCounter</code>. As you can see, all contribution blocks (coming from different fields) are assembled into the same <code>ArrayCounter</code>. The block-assembly counterpart will have the input <code>A</code> be a <code>MatrixBlock{&lt;:ArrayCounter}</code>, and assembles each contribution block to it&#39;s corresponding <code>ArrayCounter</code> (notice the <code>A.array[i,j]</code>).</p><h3 id="B)-Assembling-multiple-FE-Fields-into-the-same-Block"><a class="docs-heading-anchor" href="#B)-Assembling-multiple-FE-Fields-into-the-same-Block">B) Assembling multiple FE Fields into the same Block</a><a id="B)-Assembling-multiple-FE-Fields-into-the-same-Block-1"></a><a class="docs-heading-anchor-permalink" href="#B)-Assembling-multiple-FE-Fields-into-the-same-Block" title="Permalink"></a></h3><p>The <code>BlockMultiFieldStyle</code> constructor can take up to three parameters:</p><ol><li><code>NB</code> :: Integer, representing the number of final blocks. Then the matrix and vector will have <code>NBxNB</code> and <code>NB</code> blocks respectively.</li><li><code>SB</code> :: Tuple of integers, of length <code>NB</code>. In each position, <code>SB[ib]</code> is the number of fields that will be assembled in that block.</li><li><code>P</code> :: Tuple of integers, of length the number of fields. This represents a field permutation, such that the fields will be reordered as<code>[P[1],P[2],....,P[n]]</code>.</li></ol><p>Using this three parameters, one can assemble an arbitrary number of fields into any number of blocks.</p><p><strong>Example</strong>: Consider we are solving an MHD problem with variables <code>(u,p,j,q)</code> , i.e (fluid velocity, fluid pressure, magnetic current, electric potential). Although the variables are in this specific order in the <code>MultiFieldFESpace</code>, we want to build a block-preconditioner that solves <code>(u,j)</code> together in a single block then <code>p</code> and <code>q</code> separately in two other blocks. Then we would need to assemble our system using <code>NB=3</code>, <code>SB=(2,1,1)</code> and <code>P=(1,3,2,4)</code>. With this configuration, we will create 3 blocks. The first block will have size 2 and hold variables <code>[P[1],P[2]] = [1,3] = [u,j]</code>. The second block will have size 1 and hold variables <code>[P[3]] = [2] = [p]</code>. Finally, the third block will hold variables <code>[P[4]] = [4] = [q]</code>.</p><p>In terms of implementation, everything is the same. We use <code>ArrayBlockViews</code> (which is a view counterpart of <code>ArrayBlock</code>) so that an array of <code>NBxNB</code> array builders / array counters can be indexed using the field indexes. This allows us to use the same dispatches as we had in part A.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Adaptivity/">« Gridap.Adaptivity</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 2 November 2023 22:41">Thursday 2 November 2023</span>. Using Julia version 1.8.5.</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>Getting Started · Gridap.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-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"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="Gridap.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">Gridap.jl</span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Getting Started</a><ul class="internal"><li><a class="tocitem" href="#Installation-requirements"><span>Installation requirements</span></a></li><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Further-steps"><span>Further steps</span></a></li></ul></li><li><a class="tocitem" href="../Gridap/">Gridap</a></li><li><a class="tocitem" href="../Helpers/">Gridap.Helpers</a></li><li><a class="tocitem" href="../Io/">Gridap.Io</a></li><li><a class="tocitem" href="../Algebra/">Gridap.Algebra</a></li><li><a class="tocitem" href="../Arrays/">Gridap.Arrays</a></li><li><a class="tocitem" href="../TensorValues/">Gridap.TensorValues</a></li><li><a class="tocitem" href="../Fields/">Gridap.Fields</a></li><li><a class="tocitem" href="../Polynomials/">Gridap.Polynomials</a></li><li><a class="tocitem" href="../ReferenceFEs/">Gridap.ReferenceFEs</a></li><li><a class="tocitem" href="../Geometry/">Gridap.Geometry</a></li><li><a class="tocitem" href="../CellData/">Gridap.CellData</a></li><li><a class="tocitem" href="../Visualization/">Gridap.Visualization</a></li><li><a class="tocitem" href="../FESpaces/">Gridap.FESpaces</a></li><li><a class="tocitem" href="../MultiField/">Gridap.MultiField</a></li><li><a class="tocitem" href="../Adaptivity/">Gridap.Adaptivity</a></li><li><span class="tocitem">Developper notes</span><ul><li><a class="tocitem" href="../dev-notes/block-assemblers/">Block Assemblers</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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Getting Started</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Getting Started</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/gridap/Gridap.jl/blob/master/docs/src/getting-started.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Getting-Started"><a class="docs-heading-anchor" href="#Getting-Started">Getting Started</a><a id="Getting-Started-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-Started" title="Permalink"></a></h1><h2 id="Installation-requirements"><a class="docs-heading-anchor" href="#Installation-requirements">Installation requirements</a><a id="Installation-requirements-1"></a><a class="docs-heading-anchor-permalink" href="#Installation-requirements" title="Permalink"></a></h2><p>Gridap is tested on Linux, but it should be also possible to use it on Mac OS and Windows since it is written exclusively in Julia and it only depends on registered Julia packages.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>Gridap is a registered package. Thus, the installation should be straight forward using the Julia&#39;s package manager <a href="https://julialang.github.io/Pkg.jl/v1/">Pkg</a>. To this end, open the Julia REPL (i.e., execute the <code>julia</code> binary), type <code>]</code> to enter package mode, and install Gridap as follows</p><pre><code class="language-julia">pkg&gt; add Gridap</code></pre><p>That&#39;s all.</p><p>For further information about how to install and manage Julia packages, see the <a href="https://julialang.github.io/Pkg.jl/v1/">Pkg documentation</a>.</p><h2 id="Further-steps"><a class="docs-heading-anchor" href="#Further-steps">Further steps</a><a id="Further-steps-1"></a><a class="docs-heading-anchor-permalink" href="#Further-steps" title="Permalink"></a></h2><p>We recommend to follow the <a href="https://gridap.github.io/Tutorials/dev/">Gridap Tutorials</a> in order to get familiar with the library.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../Gridap/">Gridap »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Monday 16 October 2023 07:18">Monday 16 October 2023</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Getting Started · Gridap.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.0/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-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"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="Gridap.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">Gridap.jl</span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Getting Started</a><ul class="internal"><li><a class="tocitem" href="#Installation-requirements"><span>Installation requirements</span></a></li><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Further-steps"><span>Further steps</span></a></li></ul></li><li><a class="tocitem" href="../Gridap/">Gridap</a></li><li><a class="tocitem" href="../Helpers/">Gridap.Helpers</a></li><li><a class="tocitem" href="../Io/">Gridap.Io</a></li><li><a class="tocitem" href="../Algebra/">Gridap.Algebra</a></li><li><a class="tocitem" href="../Arrays/">Gridap.Arrays</a></li><li><a class="tocitem" href="../TensorValues/">Gridap.TensorValues</a></li><li><a class="tocitem" href="../Fields/">Gridap.Fields</a></li><li><a class="tocitem" href="../Polynomials/">Gridap.Polynomials</a></li><li><a class="tocitem" href="../ReferenceFEs/">Gridap.ReferenceFEs</a></li><li><a class="tocitem" href="../Geometry/">Gridap.Geometry</a></li><li><a class="tocitem" href="../CellData/">Gridap.CellData</a></li><li><a class="tocitem" href="../Visualization/">Gridap.Visualization</a></li><li><a class="tocitem" href="../FESpaces/">Gridap.FESpaces</a></li><li><a class="tocitem" href="../MultiField/">Gridap.MultiField</a></li><li><a class="tocitem" href="../Adaptivity/">Gridap.Adaptivity</a></li><li><span class="tocitem">Developper notes</span><ul><li><a class="tocitem" href="../dev-notes/block-assemblers/">Block Assemblers</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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Getting Started</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Getting Started</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/gridap/Gridap.jl/blob/master/docs/src/getting-started.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Getting-Started"><a class="docs-heading-anchor" href="#Getting-Started">Getting Started</a><a id="Getting-Started-1"></a><a class="docs-heading-anchor-permalink" href="#Getting-Started" title="Permalink"></a></h1><h2 id="Installation-requirements"><a class="docs-heading-anchor" href="#Installation-requirements">Installation requirements</a><a id="Installation-requirements-1"></a><a class="docs-heading-anchor-permalink" href="#Installation-requirements" title="Permalink"></a></h2><p>Gridap is tested on Linux, but it should be also possible to use it on Mac OS and Windows since it is written exclusively in Julia and it only depends on registered Julia packages.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>Gridap is a registered package. Thus, the installation should be straight forward using the Julia&#39;s package manager <a href="https://julialang.github.io/Pkg.jl/v1/">Pkg</a>. To this end, open the Julia REPL (i.e., execute the <code>julia</code> binary), type <code>]</code> to enter package mode, and install Gridap as follows</p><pre><code class="language-julia">pkg&gt; add Gridap</code></pre><p>That&#39;s all.</p><p>For further information about how to install and manage Julia packages, see the <a href="https://julialang.github.io/Pkg.jl/v1/">Pkg documentation</a>.</p><h2 id="Further-steps"><a class="docs-heading-anchor" href="#Further-steps">Further steps</a><a id="Further-steps-1"></a><a class="docs-heading-anchor-permalink" href="#Further-steps" title="Permalink"></a></h2><p>We recommend to follow the <a href="https://gridap.github.io/Tutorials/dev/">Gridap Tutorials</a> in order to get familiar with the library.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../Gridap/">Gridap »</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 2 November 2023 22:41">Thursday 2 November 2023</span>. Using Julia version 1.8.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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