Jocelyn Etienne – research<p>I'm wondering: <a href="https://mathstodon.xyz/tags/physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>physics</span></a> makes a lot of use of <a href="https://mathstodon.xyz/tags/periodic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>periodic</span></a> functions, in particular it is very useful to solve space-dependent equations in representative volumes with <a href="https://mathstodon.xyz/tags/periodicBoundaryConditions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>periodicBoundaryConditions</span></a>.</p><p>However I've only seen it done with periodicity along orthogonal directions, aligned with a Cartesian frame.</p><p>Do you know of work, e.g. <a href="https://mathstodon.xyz/tags/PDE" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PDE</span></a> resolution, in nonrectangular <a href="https://mathstodon.xyz/tags/periodicDomains" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>periodicDomains</span></a>? E.g., in a <a href="https://mathstodon.xyz/tags/tiled" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>tiled</span></a> hexagon? (but with a sufficiently generic setting, not exploiting regular hexagon symmetries) Even better if the periodicity parameters themselves are among the unknowns.</p><p>(Maybe I'm completely missing something obvious there, I'm in my first steps towards defining what I want - any random thought on the topic highly welcome!)</p><p><a href="https://mathstodon.xyz/tags/tiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>tiling</span></a> people?</p>