band(2rheolef)

💖 band — the banded level set method 💖

okay bestie, listen up — this is a rheolef-7.2 situation and it's lowkey iconic, so let's get into it.

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✨ NAME ✨

band — the banded level set method, straight outta rheolef-7.2 🎀

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🦋 DESCRIPTION 🦋

So picture this: you've got fh, right? It's a finite element function defined on a geometric domain Lambda. And the set of elements that intersect the zero level set — that's

{x in Lambda, fh(x) = 0}

— is what we call a band. periodt. 💅

This class represents exactly that band. What's it for, you ask? It's for solving problems defined on a surface, when the surface itself is implicitly defined by a level_set(3) function. No cap, that's the whole vibe. 🌸

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🌈 ACESSORS 🌈

Every single side in the surface mesh — the one you get back from the level_set member function — is included into an element of the band mesh, which you get back from the band member function. the way they correspond... obsessed. ✨

And here's the part that's giving main character energy: in the distributed memory environment, this correspondence lives on the same local memory. So local indexes are totally fine to use for it. The whole thing is provided by the sid_ie2bnd_ie member function. iykyk 🫶

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👑 TOPOLOGY AND DOMAINS 👑

For the direct resolution of systems posed on the band, the mesh returned by the band() member function provides some domains of vertices. Let's break it down, bestie:

• The 'zero' vertex domain lists all vertices xi such that fh(xi)=0. 🍓
• The 'isolated' vertex domain lists all vertices xi such that fh(xi)!=0 and xi is contained by only one element K and all vertices xj!=xi of K satisfies fh(xj)=0. (yeah it's a mouthful, but it's exactly right 💀)
• The others — the vertices of the band that get separated by the zero and isolated ones — are organized by connected components. The n_connex_component member function returns how many there are. 🔥

The corresponding vertex domains of the band are named 'cci' where i should be replaced by any number between 0 and n_connex_component-1. So like cc0, cc1, etc. cute naming scheme fr fr. 🎀

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💅 IMPLEMENTATION 💅

This documentation has been generated from file main/lib/band.h 📄

The band class is simply an alias to the band_basic class:

typedef band_basic<Float> band;

The band_basic class provides an interface, via the smart_pointer(7) class family, to a mesh container:

template <class T, class M = rheo_default_memory_model>
class band_basic {
public:

  typedef typename geo_basic<T,M>::size_type size_type;

// allocators:

  band_basic();
  band_basic(const field_basic<T,M>& fh,
    const level_set_option& opt = level_set_option());

// accessors:

  const geo_basic<T,M>& band() const { return _band; }
  const geo_basic<T,M>& level_set() const { return _gamma; }
  size_type sid_ie2bnd_ie (size_type sid_ie) const { return _sid_ie2bnd_ie [sid_ie]; }
  size_type n_connected_component() const { return _ncc; }

};

look at that struct definition. she's beautiful. she's everything. 🌟

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🌸 AUTHOR 🌸

Pierre Saramito <Pierre.Saramito@imag.fr> 💌

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⭐ COPYRIGHT ⭐

Copyright (C) 2000-2018 Pierre Saramito <Pierre.Saramito@imag.fr> GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>. This is free software: you are free to change and redistribute it. There is NO WARRANTY, to the extent permitted by law.

fr fr, no warranty — read that part twice bestie, it's not a drill 😭

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and that's the whole page, babe — this was rheolef, Version 7.2, and you just read the band(2rheolef) manual. slay, ate, left no crumbs. go solve a surface problem, you got this 💖✨🦋