Outline

Outline

Unfitted Finite Elements

Unfitted Geometries

Long term goals

My PhD Thesis:

Outline

Gridap and Julia

Cell-wise intersection

Achievements: Robustness

Achievements: Robustness

Achievements: Parallel Scalability

Outline

Using STLCutters.jl

] add STLCutters                                     

git clone https://github.com/gridap/STLCutters.jl.git

Distributed usage

mpiexec -np 8 julia example.jl

] add GridapP4est

Distributed usage

Adaptive Mesh Refinement (AMR)

flags = adapt_cut_cells(parts,cutgeo)
model, = Gridap.Adaptivity.adapt(model,flags)
cutgeo = cut(model,geo)

Coding style

• Gridap-like coding style

• Semantic Versioning: Julia registry, registered dependencies

• GitHub Utilities: Issues, PRs, CI

• Documentation: docstrings, documentation pages

Code structure

Code structure

Package files

src/: 5k code lines
├── STLCutters.jl: Main module with imports and exports
├── SubTriangulations.jl: Core of the package with main algorithms
├── STLs.jl: Load, clean and manage STL geometries
├── Polyhedra.jl: General polytope operations
├── SimplexFaces.jl: Geometrical operations on simplicies
├── Embedded.jl: Extending GridapEmbedded API
└── Distributed.jl: Extending distributed functions and algorithms

Core procedures

function subtriangulate(stl,bgmodel)
c_to_f = compute_cell_to_facets(bgmodel,stl)
submesh = _empty_submesh()
for cell in findall(!isempty,c_to_f)
    Γ = stl[c_to_f[cell]]
    P = compute_polyhedra(cell,bgmodel,Γ)
    save_cell_submesh!(submesh,cell,P...)
end
propagate_inout!(submesh)
delete_small_cells(submesh)
grids = compute_grids(submesh)
labels = SubtriangulationLabels(submesh)
return grids,labels
end

function compute_polyhedra(cell,bgmodel,Γ)
K = Polyhedron(bgmodel,cell)
Γk = clip(Γ,planes(K))  
Kin,Kout = refine(K,planes(Γk),reflex_planes(Γk))
return Kin,Kout,Γk
end

function save_cell_submesh!(submesh,cell,Kin,Kout,Γk)
_submesh,_face_submesh = submesh
append!(_submesh,cell,simplexify(Kin),simplexify(Kout))
append!(_face_submesh,cell,simplexify(Γk))
end

Some functions have been simplified for demonstration purposes

Outline

Future Work

• Extract mesh of general polytopes STLCutters.jl#37

• Reduce memory allocations STLCutters.jl#38

• Deal with disconnected subdomains STLCutters.jl

• Distribute space-time methods STLCutters.jl

• AMR with unfitted AgFEM GridapEmbedded.jl

• Fix moment fitting in parallel GridapEmbedded.jl#94

• Solve void subdomains GridapDistributed.jl

• Test distributed solvers on unfitted FSI

Acknowledgments

• Special acknowledgments:

  • Supervisors: Santiago Badia & Francesc Verdugo
  • Contributors: STLCutters & Gridap ecosystem
  • Users
  • You

• Thanks for giving a star on GitHub

Hands-on & Questions

• Visit the GitHub page: https://github.com/gridap/STLCutters.jl

• Check the documentation: https://gridap.github.io/STLCutters.jl

• Locally navigate the repository & run examples:

git clone https://github.com/gridap/STLCutters.jl.git
code STLCutters.jl

julia> include("examples/LinearElasticity.jl")
julia> filename = "test/data/550964.stl"
julia> LinearElasticity.main(filename,n=50,force=(tand(5),0,-1),output="example4")