CREATIVE FREEDOM FOR COMPUTATIONAL MESH GENERATION IN DEAL.II Nicola - - PowerPoint PPT Presentation

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CREATIVE FREEDOM FOR COMPUTATIONAL MESH GENERATION IN DEAL.II Nicola - - PowerPoint PPT Presentation

May 27, 2023 286 likes •504 views

CREATIVE FREEDOM FOR COMPUTATIONAL MESH GENERATION IN DEAL.II Nicola Giuliani , Luca Heltai (ngiuliani@sissa.it) Sixth deal.II Users and Developers Workshop MESH GENERATION Mesh generation a secret of the darkest arts An accurate mesh

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CREATIVE FREEDOM FOR COMPUTATIONAL MESH GENERATION IN DEAL.II

Sixth deal.II Users and Developers Workshop Nicola Giuliani, Luca Heltai (ngiuliani@sissa.it)

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N.Giuliani Creative Freedom in deal.II

MESH GENERATION

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Mesh generation … a secret of the darkest arts ▸ An accurate mesh is a prerogative require of an

accurate simulation

▸ Mesh generator gets very expensive very quickly ▸ CAD files: engineeringly accurate and engineeringly

limited

Let’s look somewhere else…

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N.Giuliani Creative Freedom in deal.II

3D MODELLING TOOLS

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3D modelling tools offer the possibility of creating complex geometries in a very straightforward way (relative definition).

▸ Used in computer graphics (video-gaming, animation

studios), enormous users community and opportunities

▸ Produce smooth surfaces exploiting the subdivision

surface algorithm (Catmull-Clark 1978)

▸ The algorithm is a generalisation of bi-cubic uniform B-

spline surfaces to arbitrary topology

Bridge computer graphics and scientific computing may not be such a bad idea…

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N.Giuliani Creative Freedom in deal.II

CATMULL CLARK SUBDIV

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▸ Recursive algorithm ▸ Refinement based on

neighbouring faces/edges/ vertices

▸ Each new point is created using an

“average” of face points and edges.

▸ The limit surface of Catmull–Clark

subdivision surfaces can also be evaluated directly, without any recursive refinement.

▸ Little scientific literature

(opportunities)

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N.Giuliani Creative Freedom in deal.II

LET’S SEE IT…

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“Know averaging? You know enough to work at Pixar” 
 Tony De Rose Ted-ED talk

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N.Giuliani Creative Freedom in deal.II

CLICK BAITS AND APPETISERS

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Foobar Yorozuya (https://www.youtube.com/watch?v=dY0K65eXhkA ) Now version 2.79b (23rd July 12.00)

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N.Giuliani Creative Freedom in deal.II

BLENDER PROS

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▸ Free open-source software (GPL license) ▸ Straightforward mesh generation using a GUI ▸ Developed and scriptable in Python 3 ▸ Constantly increasing users’ community (2017: +6.5

millions downloads)

▸ Reasonably good documentation ▸ BlenderStackExchange ▸ Youtube channels: at least three are official ▸ Very catchy results (made for artists and small teams)

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N.Giuliani Creative Freedom in deal.II

BLENDER AND DEAL.II NOW

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▸ Readable geometries using the Open-Asset-IMPorter-Lib

(ASSIMP), introduced by deal2lkit and now in deal.II

▸ Blender generates surface geometries and those can be

imported in deal.II

▸ Codimension zero/one problem with Blender geometries

solvable in deal.II, dim = 1,2 spacedim = 2, 3

▸ Possibility of non trivial geometries for scientific

computing

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N.Giuliani Creative Freedom in deal.II

CREATE A NOT SO STUPID MESH

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N.Giuliani Creative Freedom in deal.II

STEP-38 MONKEY CODE

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STEP-38 MONKEY RESULTS

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N.Giuliani Creative Freedom in deal.II

REAL WORKING EXAMPLE 1/2

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REAL WORKING EXAMPLE 2/2

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N.Giuliani Creative Freedom in deal.II

CATCHY RESULTS (NICOLA LEVEL)

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N.Giuliani Creative Freedom in deal.II

CATCHY RESULTS (LUCA LEVEL)

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We are just scratching the surface

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N.Giuliani Creative Freedom in deal.II

PRESENT SITUATION SUMMARY

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▸ Generation of complex geometry using Blender ▸ Import of the geometries directly in deal.II ▸ Creation of codim-1 surfaces in 3D ▸ Creation of codim-0/1 surfaces in 2D Blender only creates curves and surfaces so only those can be imported directly in deal.II

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N.Giuliani Creative Freedom in deal.II

DEAL.II AND BLENDER IN THE FUTURE

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▸ Definition and implementation of new Manifold using

the geometry exported from Blender (interpolating polynomials)

▸ Introduction of the Catmull-Clark algorithm in the

library to have a high order mapping capable of smooth surfaces

▸ Expand the connections between deal.II and the 3D

modelling world

We can look beyond Blender to search for something more deal.II oriented We need to overcome the codim-1 limitation in 3D

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N.Giuliani Creative Freedom in deal.II

LET’S LOOK BIG

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N.Giuliani Creative Freedom in deal.II

OPENSUBDIV

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OpenSubdiv is a set of open source libraries that implement high performance subdivision surface (subdiv) evaluation on massively parallel CPU and GPU architectures.

▸ Massively parallel implementation of Catmull-Clark algorithm ▸ Developed and freely available in C++ ▸ Released under Apache license ▸ Fairly reliable developers (Pixar Animation studios)

http://graphics.pixar.com/opensubdiv/docs/intro.html https://github.com/PixarAnimationStudios/OpenSubdiv

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N.Giuliani Creative Freedom in deal.II

REFERENCES

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Questions? Curiosities? Feel free to ask anything (ngiuliani@sissa.it, heltai@sissa.it)

  • N. Giuliani. Modelling Fluid Structure Interaction problems using

Boundary Element Method. PhD thesis, SISSA, Scuola Internazionale Superiore di Studi Avanzati, 2017.

  • https://www.blender.org/
  • https://www.youtube.com/