# \[ANN\] Gridap.jl: A feature-rich Finite Element ecosystem 100% in Julia

**URL:** <https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824>\
**Category:** Package Announcements\
**Tags:** package, announcement, pde, fem\
**Created:** [July 10, 2020, 5:59am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824 "2020-07-10T05:59:30Z")\
**Posts on this page:** 20\
**Page:** 1

<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 5:59am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/1 "2020-07-10T05:59:30Z")

</div>

We (@santiagobadia and @fverdugo) are happy to announce [Gridap.jl](https://github.com/gridap/Gridap.jl) a new Finite Element framework written in Julia for the numerical simulation of a wide range of mathematical models governed by partial differential equations (PDEs).

Gridap.jl is designed with three main purposes:

- to help application experts to easily simulate complex PDE-based real world problems
- to help researchers improve productivity when developing new Finite Element techniques
- and also for its usage in numerical PDE courses

## What can Gridap.jl do ?

Gridap is able to solve different types of PDEs:

- linear and nonlinear
- Steady state, state-dependent, and time-dependent
- Single field and multi-physics
- PDEs in 1D, 2D, 3D, 4D, 5D, …

with different types of Finite Element techniques:

- Continuous and Discontinuous Galerkin methods
- Grad, div, and curl-conforming interpolations of arbitrary order
- Embedded Finite Elements (AgFEM and CutFEM)

that can easily be extended.

## Why Gridap.jl ?

The main motivation behind Gridap.jl is to find an improved balance between computational performance, user-experience and work-flow productivity, when working with Finite Element libraries. To this end, the library design is based on lazy data-structures that represent objects (e.g., elemental matrices and vectors) on the entire computational domain. This allows us the library developers to hide assembly loops and other core computations from the user-code leading to a very compact, user-friendly, syntax, while providing a high degree of flexibility to users to define their own FE solvers.

For instance a Poisson problem can be solved with Gridap.jl in few lines of code by using the different abstractions provided by the library:

```julia
using Gridap
# FE mesh (aka discrete model)
url = "https://raw.githubusercontent.com/gridap/Tutorials/master/models/model.json"
model = DiscreteModelFromFile(download(url,"model.json"))
# Test and trial FE spaces
order = 2; V0 = TestFESpace(
  reffe=:Lagrangian, order=order, valuetype=Float64,
  conformity=:H1, model=model, dirichlet_tags="sides")
g(x) = 2.0; Ug = TrialFESpace(V0,g)
# Volume terms
trian_Ω = Triangulation(model)
degree = 2*order; quad_Ω = CellQuadrature(trian_Ω,degree)
a_Ω(u,v) = ∇(v)⋅∇(u); b_Ω(v) = v
t_Ω = AffineFETerm(a_Ω,b_Ω,trian_Ω,quad_Ω)
# Neumann terms
neumanntags = ["circle", "triangle", "square"]
trian_Γ = BoundaryTriangulation(model,neumanntags)
quad_Γ = CellQuadrature(trian_Γ,degree)
h(x) = 3.0; b_Γ(v) = v*h
t_Γ = FESource(b_Γ,trian_Γ,quad_Γ);
# FE problem and solution
op = AffineFEOperator(Ug,V0,t_Ω,t_Γ)
solver = LinearFESolver(LUSolver())
uh = solve(solver,op)
# Output file for visualization
writevtk(trian_Ω,"results",cellfields=["uh"=>uh])

```

 ![fig_uh](https://global.discourse-cdn.com/julialang/original/3X/7/0/70bf278a0ace7a5e41aa6c007026ac9ad81f93c3.png)

## How to start ?

If you are further interested in the project, visit the [Gridap.jl](https://github.com/gridap/Gridap.jl) repository.

If you want to start learning how to solve PDEs with Gridap.jl, then visit our [Tutorials](https://github.com/gridap/Tutorials) repository.

---

<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [July 10, 2020, 8:07am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/2 "2020-07-10T08:07:35Z")

</div>

Thanks for sharing this great package! Could you please say a word about how Gridap differs from JuliaFEM, FinEtools and JuAFEM?

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<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 8:44am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/3 "2020-07-10T08:44:50Z")

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Each Finite Element library is unique in some way with its own features. This is like with text editors, you cannot say that X can replace Y.

In any case, Gridap is a quite large project with a decent amount of functionality ready to be used in different scenarios.

Perhaps the distinctive feature is the use of lazy arrays to work with cell-wise data and the compact user API, which is as compact as FEniCs but 100% in julia.

---

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**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [July 10, 2020, 8:50am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/4 "2020-07-10T08:50:31Z")

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A diplomatic answer 😄 Anyways, always good to see more high quality FEA packages! So how easy or difficult would you say it is to implement some basic topology optimization on top of Gridap?

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**Author:** ![mauro3](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mauro3/32/292_2.png) [@mauro3](https://discourse.julialang.org/u/mauro3)\
**Post date:** [July 10, 2020, 8:54am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/5 "2020-07-10T08:54:17Z")

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Really impressive docs!

What about time dependent problems? Integration with DiffEq framework?

Also, if it is similar in functionality to Fenics, then that would be a useful thing to state in the Readme, as Fenics is so widely known.

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<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 8:57am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/6 "2020-07-10T08:57:49Z")

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> So how easy or difficult would you say it is to implement some basic topology optimization on top of Gridap?!

It should be possible. If you are familiar with topology optimization, we can collaborate to write a short tutorial on TO with gridap

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<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [July 10, 2020, 8:59am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/7 "2020-07-10T08:59:04Z")

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> [@fverdugo](#):
>
> If you are familiar with topology optimization, we can collaborate to write a short tutorial on TO with gridap

Sounds good. I can maybe support Gridap in [GitHub - JuliaTopOpt/TopOpt.jl: A package for binary and continuous, single and multi-material, truss and continuum, 2D and 3D topology optimization on unstructured meshes using automatic differentiation in Julia.](https://github.com/mohamed82008/TopOpt.jl).

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**Author:** ![santiagobadia](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/santiagobadia/32/7792_2.png) [@santiagobadia](https://discourse.julialang.org/u/santiagobadia)\
**Post date:** [July 10, 2020, 9:02am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/8 "2020-07-10T09:02:24Z")

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We can do time integration (method of lines)

[https://github.com/gridap/GridapODEs.jl](https://github.com/gridap/GridapODEs.jl)

and we are developing some tutorials.

The coupling with DiffEq is ongoing work, we have just some preliminary results.

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<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 9:06am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/9 "2020-07-10T09:06:52Z")

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> [@mohamed82008](#):
>
> I can maybe support Gridap in [GitHub - JuliaTopOpt/TopOpt.jl: A package for binary and continuous, single and multi-material, truss and continuum, 2D and 3D topology optimization on unstructured meshes using automatic differentiation in Julia.](https://github.com/mohamed82008/TopOpt.jl).

If you specify which are the inputs and outputs you need from a FE solver, I can say how this is done in Gridap.

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<div class="post-metadata">

**Author:** ![mohamed82008](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mohamed82008/32/18171_2.png) [@mohamed82008](https://discourse.julialang.org/u/mohamed82008)\
**Post date:** [July 10, 2020, 9:09am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/10 "2020-07-10T09:09:47Z")

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For now, TopOpt is based on JuAFEM. I want to abstract away the FEA backend though to enable supporting other packages. Once I have a minimal interface, let’s have this discussion again, hopefully soon!

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**Author:** ![retrosnub](https://avatars.discourse-cdn.com/v4/letter/r/ecb155/32.png) [@retrosnub](https://discourse.julialang.org/u/retrosnub)\
**Post date:** [July 10, 2020, 10:29am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/11 "2020-07-10T10:29:01Z")

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I’ve actually found this package a bit earlier on this [survey site](https://github.com/JuliaPDE/SurveyofPDEPackages#fem), impressive work!  
A few remarks:

- I noticed `Gridap.TensorValues` that subtype `Number` to have broadcasted operations work nicely, have you considered using the julia `Ref()` on normal arrays instead of introducing a new abstraction? The reason being that many methods that people have implemented on `AbstractArrays` can then be reused in a pointwise manner.
- Last time I tried, I remember there was no easy way to create the grid without importing a mesh-file (relying on gmsh). Do you consider domain specification and meshing out of scope for your package or have you considered adding some primitives there? I realize `GridapGmsh` covers this somewhat but it seems more like a low-level interface to gmsh.
- How easy is it to hook into the assembly/solve phase? Can one for example implement dof-reorderings or other preconditioners easily?
- Skimming the codebase, I noticed that the finite element types are hard-coded in quite a few places (namely in dof-mappings). Can you comment on how hard it would be to add a new custom finite element (nodal basis, reference-element-mapped)?

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<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 10:55am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/12 "2020-07-10T10:55:40Z")

</div>

> Last time I tried, I remember there was no easy way to create the grid without importing a mesh-file (relying on gmsh). Do you consider domain specification and meshing out of scope for your package or have you considered adding some primitives there? I realize `GridapGmsh` covers this somewhat but it seems more like a low-level interface to gmsh.

Mesh generation is definitively out-of-scope. We only provide a simple Cartesian mesh generator for convenience. Unstructured grids are generated elsewhere. If you have a `msh` file generated with GMSH, then you can read it with function `GmshDiscreteModel` provided by the [GridapGmsh.jl](https://github.com/gridap/GridapGmsh.jl) package (we have tested for linear triangles and tets). The other option is to avoid generating unstructured meshes and use embedded FEM. This can be done with [GridapEmbedded.jl](https://github.com/gridap/GridapEmbedded.jl). Here, you can specify your geometry as bolean operations between simple shapes.

---

<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 11:05am UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/13 "2020-07-10T11:05:28Z")

</div>

> [@retrosnub](#):
>
> Skimming the codebase, I noticed that the finite element types are hard-coded in quite a few places (namely in dof-mappings). Can you comment on how hard it would be to add a new custom finite element (nodal basis, reference-element-mapped)?

I don’t know if I have understood it correctly, but I think this is not true. Finite element types are not hard-coded. The code is implemented in terms of an abstract type called `ReferenceFE` which can be extended with custom user-defined concrete implementations. It is true that the library provides a default local-to-global dof map, but you can implement you own if you wish. You just need to implement a new constructor `FESpaceWithMyOwnDOFMap` that should return some object with a well defined interface.

---

<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 10, 2020, 12:18pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/14 "2020-07-10T12:18:15Z")

</div>

> [@retrosnub](#):
>
> How easy is it to hook into the assembly/solve phase? Can one for example implement dof-reorderings or other preconditioners easily?

Yes, you can use the linear solver you want. For instance, for the example above you can do:

```julia
op = AffineFEOperator(Ug,V0,t_Ω,t_Γ)
A = get_matrix(op)
b = get_vector(op)
x = A\b # Solve this with your favorite linear solver
uh = FEFunction(Ug,x)
writevtk(trian_Ω,"results",cellfields=["uh"=>uh])

```

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<div class="post-metadata">

**Author:** ![PetrKryslUCSD](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/petrkryslucsd/32/215825_2.png) [@PetrKryslUCSD](https://discourse.julialang.org/u/PetrKryslUCSD)\
**Post date:** [July 10, 2020, 2:52pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/15 "2020-07-10T14:52:47Z")

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I noticed that at least one member of this forum found Gridap.jl in the [PDE-software list](https://github.com/JuliaPDE/SurveyofPDEPackages)  
prior to this announcement!

That is great, and so I would like to invite all of you: include your work in the list, it seems to provide good exposure. Your software may come in handy in someone else’s work. Do let them know of its existence. File an issue, or open a PR.  
Thanks,  
P

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**Author:** ![juliohm](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/juliohm/32/215266_2.png) [@juliohm](https://discourse.julialang.org/u/juliohm)\
**Post date:** [July 10, 2020, 6:18pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/16 "2020-07-10T18:18:36Z")

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Amazing work! Thank you for this great contribution Gridap.jl authors!

I’d like to jump in and share another standardization effort that is ongoing regarding meshes for FEM, spatial modeling and visualization: [https://github.com/JuliaGeometry/GeometryBasics.jl/issues/15](https://github.com/JuliaGeometry/GeometryBasics.jl/issues/15)

A prototype a la [Tables.jl](https://github.com/JuliaData/Tables.jl) is being sketched in [Meshes.jl](https://github.com/JuliaGeometry/Meshes.jl). Ultimately, we would like to benefit from a common interface so that we can operate on mesh objects within different frameworks.

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<div class="post-metadata">

**Author:** ![B\_W\_Harris](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/b_w_harris/32/4112_2.png) [@B\_W\_Harris](https://discourse.julialang.org/u/B_W_Harris)\
**Post date:** [July 15, 2020, 1:30pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/17 "2020-07-15T13:30:34Z")

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This seems like a very nice package with good documentation and tutorials. Thank you.

I’ve run through the tutorial set without trouble. However, when I attempt create my own model.json file, as described in Tutorial 1 notebook as:

“The file `"model.json"` is a regular `json` file that includes a set of fields that describe the discrete model. It was generated by using together the [GMSH](http://gmsh.info/) mesh generator and the [GridapGmsh](https://github.com/gridap/GridapGmsh.jl) package. First, we generate a `"model.msh"` file with GMSH (which contains a FE mesh and information about user-defined physical boundaries in {GMSH} format). **Then, this file is converted to the Gridap-compatible `"model.json"` file using the conversion tools available in the GridapGmsh package.** See the documentation of the [GridapGmsh](https://github.com/gridap/GridapGmsh.jl) for more information.”

I get stuck at the GridapGmsh step. I don’t see any tools in there (documentation or source code) to perform the conversion. Can you point me in the right direction?

---

<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 15, 2020, 6:31pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/18 "2020-07-15T18:31:29Z")

</div>

Thanks for the interest! Try this:

using Gridap  
using [Gridap.Io](http://Gridap.Io)  
using GridapGmsh

model = GmshDiscreteModel(“model.msh”)

fn = “model.json”  
to\_json\_file(model,fn)

---

<div class="post-metadata">

**Author:** ![B\_W\_Harris](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/b_w_harris/32/4112_2.png) [@B\_W\_Harris](https://discourse.julialang.org/u/B_W_Harris)\
**Post date:** [July 15, 2020, 7:03pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/19 "2020-07-15T19:03:38Z")

</div>

Ah yes thank you. That’s the kick I needed. I see now that it’s in the tutorial/models folder for each of the model .jl files.

---

<div class="post-metadata">

**Author:** ![fverdugo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fverdugo/32/9446_2.png) [@fverdugo](https://discourse.julialang.org/u/fverdugo)\
**Post date:** [July 15, 2020, 7:13pm UTC](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824/20 "2020-07-15T19:13:32Z")

</div>

Nice that it helps!

BTW, you can use the object “model” directly in your computation without writing it to json and reading it again. We only use the json file in the tutorials as a way of avoinding to force the users to install gmsh.

[Next page](https://discourse.julialang.org/t/ann-gridap-jl-a-feature-rich-finite-element-ecosystem-100-in-julia/42824.md?page=2)