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<!DOCTYPE html>
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<title>Animate, Movement, Goalie and UM2N — Animate, Movement, Goalie and UM2N 0.1 documentation</title>
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<section id="welcome-to-the-documentation-for-animate-movement-goalie-and-um2n">
<h1>Welcome to the documentation for Animate, Movement, Goalie and UM2N!<a class="headerlink" href="#welcome-to-the-documentation-for-animate-movement-goalie-and-um2n" title="Link to this heading">¶</a></h1>
<p><a class="reference external" href="https://mesh-adaptation.github.io/docs/animate/index.html">Animate</a> is a package which provides anisotropic mesh adaptation
functionality for the Python-based finite element library
<a class="reference external" href="http://www.firedrakeproject.org/">Firedrake</a>. Given an initial mesh, the
user defines a Riemannian metric field (or simply ‘metric’), which provides the
‘optimal mesh concept’, i.e. a ‘blueprint’ for what adapted meshes will look
like. Animate can then be used to transform the initial mesh into an adapted
mesh, making use of the metric to guide the transformations.</p>
<p><a class="reference external" href="https://mesh-adaptation.github.io/docs/movement/index.html">Movement</a> focuses on alternative mesh adaptation strategies to
the metric-based approach of Animate. Where Animate allows degrees of freedom to be
added and removed from the input mesh in order to obtain an adapted mesh, Movement is
concerned only with <em>mesh movement</em> methods, which simply move degrees of freedom
around. In some cases the first approach is more suitable; in some cases the latter.
Several different strategies are implemented within Movement.</p>
<p><a class="reference external" href="https://mesh-adaptation.github.io/docs/goalie/index.html">Goalie</a> is more of an ‘outer-loop’ package and is focused on a
goal-oriented mesh adaptation pipeline for solving partial differential
equations (PDEs) using adapted meshes. Goalie supports solving time-dependent PDEs
and their adjoints on sequences of meshes, performing goal-oriented error
estimation, and adapting the meshes in the sequence with a user-provided adaptor
function. A key example of such an adaptor function is one which uses Animate
and the metric-based approach. Goalie uses a ‘fixed-point iteration’ approach,
meaning that the PDE (and its adjoint) is solved over the whole space-time domain
whenever mesh adaptation is applied.</p>
<p><a class="reference external" href="https://mesh-adaptation.github.io/docs/UM2N/index.html">UM2N</a> is an end-to-end machine-learning based implementation of
mesh movement.</p>
<p class="rubric">Mathematical background</p>
<p>We refer to the
<a class="reference external" href="https://firedrakeproject.org/documentation.html">Firedrake documentation</a>
for an introduction to the finite element method - the discretisation approach assumed
throughout. The <cite>dolfin-adjoint</cite> package (which Goalie uses to solve adjoint problems)
contains some
<a class="reference external" href="http://www.dolfin-adjoint.org/en/latest/documentation/maths/index.html">excellent documentation</a>
on the mathematical background of adjoint problems. The metric-based mesh adaptation,
mesh movement, and goal-oriented error estimation functionalities provided by
<a class="reference external" href="https://mesh-adaptation.github.io/docs/animate/index.html">Animate</a>, <a class="reference external" href="https://mesh-adaptation.github.io/docs/movement/index.html">Movement</a>,
<a class="reference external" href="https://mesh-adaptation.github.io/docs/goalie/index.html">Goalie</a> and <a class="reference external" href="https://mesh-adaptation.github.io/docs/UM2N/index.html">UM2N</a> are described in the
respective manuals.</p>
<p class="rubric">Source code</p>
<p>The source codes for all four packages are hosted on GitHub:
<a class="reference external" href="https://github.com/mesh-adaptation/animate/">Animate</a>,
<a class="reference external" href="https://github.com/mesh-adaptation/movement/">Movement</a>,
<a class="reference external" href="https://github.com/mesh-adaptation/goalie/">Goalie</a>.
<a class="reference external" href="https://github.com/mesh-adaptation/UM2N/">UM2N</a>.</p>
<p class="rubric">Support and discussion</p>
<p>To ask for help or join discussions related to development, feel free to open issues or
start discussions on the relevant GitHub repository, or join the relevant Slack channel:
<a class="reference external" href="https://firedrakeproject.slack.com/archives/C07KTDB3JNB/">Animate</a>,
<a class="reference external" href="https://firedrakeproject.slack.com/archives/C07L7S3547M/">Movement</a>,
<a class="reference external" href="https://firedrakeproject.slack.com/archives/C07L813FG74/">Goalie</a>.
The channels are part of the
<a class="reference external" href="https://firedrakeproject.slack.com/">Firedrake Slack workspace</a>,
which is free to join.</p>
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