Update:

Development migrated to Femeko.jl

All future updates will only be available at codeberg.

Femeko.jl

Using Gmsh, Femeko simplifies the model creation and mesh generation, and provides the relevant data in a digested and simple structure.

Here is an example of how easy it is to create a model and mesh to simulate a magnet in free space with Femeko:

    cells = [] # Holds each entity (dim, tag) property     
    addRectangle([0.0,  0.0], [2.0, 1.0], cells) # 2 by 1 magnet
    ID = addDisk([0.0, 0.0], 10.0) # Disk of radius 10 with tag 'ID'
    unifyModel(cells, ID) # Combine the geometries to create a conforming mesh
    mesh = Mesh2D(cells, 2.0, 0.1) # Create a mesh with maximum element size 2.0
                                   # and with local 0.1 size mesh refinement on the magnet's boundary

    # or import your own model with
    importCAD("STEP_Models/Fennec_Fox.step")

Then, you can access the 3 nodes of the first element by nodes = mesh.t[:, 1], and the x,y coordinates of each node of that element with xy = mesh.p[:, nodes]. You also have access to the boundary elements and their respective boundary ID with mesh.surfaceT[:, elementTag], this would output the 2 nodes + boundary ID (in 2D) or 3 nodes + boundary ID (in 3D).

Femeko.jl currently has full fledged implementations for

• Magnetostatics (non-linear magnetic materials under applied fields, permanent magnets, etc)
• Heat equation (with implicit time stepping)
• Viscous fluid (incompressible, static)
• Heat transfer with convection to a passing fluid (2D)
• Micromagnetics (both in time and steepest descent energy minimization)

Femeko has implementations for both 3D and 2D in most physics packages.

Femeko.jl aims to have the following, in the future

• Full 3D Heat equation (with convection to a passing fluid)
• Elastostatics (stress)

Table of Contents

• Fully featured examples
• Installation
• C++ available implementations

Examples

Each physics package has its own folder: Magnetostatics, Micromagnetics, Heat and Fluids.

Magnetostatics

Example from Magnetostatics, the internal magnetic field of a plate aligned with the applied field.

Heat

Most implementations in Femeko have both a 2D and 3D version. Here is a snapshot of the 2D heat simulation

Fluids

Femeko.jl can incorporate quadratic order elements, solving the stokes equation of a viscus fluid for both pressure and velocity.

Micromagnetics

The Micromagnetics package has two distinct functionalities, based on the Landau-Lifshitz equation: the magnetization over time of the system; and an energy minimization by the steepest descent algorithm. The solver incorporates an external magnetic field, the demagnetizing field, the exchange field and the anisotropy field. This solver was validated against OOMMF, replicating Fig 2. of this article https://doi.org/10.1109/TMAG.2008.2001666 .

Installation

Main install:

• Open the Repl
• Press ']' key to switch to the package manager "pkg >"
• add Gmsh LinearAlgebra SparseArrays IterativeSolvers Dierckx DelimitedFiles

Most examples plot the results using Makie.jl. It is recommended that you do

• add GLMakie or/and add CairoMakie

Compiling C++ alternative implementations:

• First update your clone of the repository to include eigen by going to the terminal and run git submodule update --init --recursive while in the Femeko.jl folder
• Move to the cFemeko/Magnetostatics/ folder and compile magnetostatics.cpp with g++ -O3 -fPIC -shared -o magnetostatics.so magnetostatics.cpp
• Adding this flag is recommended: -fopenmp

Current C++ alternatives covered

Femeko has two types of C++ implementations. A full 100% rewrite to C++ and a mix between Julia and C++ with Julia's ccall(). The mixed language use has:

• Magnetostatics has a complete C++ alternative available.
• Micromagnetics has a full implementation with FEM and an older implementation with FEM-BEM.

The 100% rewrite has:

• Magnetostatics

Source code organization

Femeko is organized as:

Directory	Contents
src/	source code to handle the geometry, mesh, and FEM functionality
Fluids/	Fluid simulation implementation
Heat/	Heat simulation implementation
Magnetostatics/	Magnetostatics simulation implementation
Micromagnetics/	Micromagnetics simulation implementation
STEP_Models/	Example .STEP files to import 3D models
cFemeko/	Combined use of C++ and Julia
Femeko.cpp/	100% rewrite to C++
extern/	external libraries needed for C++ implementations

License

Distributed under the MIT License. See LICENSE for more information.