Index

ExtendableFEM

ExtendableFEM.jl is a high-level, extensible finite element method (FEM) library for Julia, supporting flexible problem descriptions, custom operators, and advanced grid management.

Features

• High-level, extensible API for solving PDE problems by finite element methods
• Flexible ProblemDescription interface for assigning unknowns and operators
• Supports custom kernel functions for bilinear, linear, and nonlinear forms
• Automatic assembly and Newton's method for NonlinearOperators
• Builds upon ExtendableGrids.jl and low level structures from ExtendableFEMBase.jl

Quick Example

The following minimal example demonstrates how to set up and solve a Poisson problem:

using ExtendableFEM
using ExtendableGrids

# Build a uniform-refined 2D unit square grid with triangles
xgrid = uniform_refine(grid_unitsquare(Triangle2D), 4)

# Create a new PDE description
PD = ProblemDescription()

# Define and assign the unknown
u = Unknown("u"; name = "potential")
assign_unknown!(PD, u)

# Assign Laplace operator (diffusion term)
assign_operator!(PD, BilinearOperator([grad(u)]; factor = 1e-3))

# Assign right-hand side data
function f!(fval, qpinfo)
    x = qpinfo.x # global coordinates of quadrature point
    fval[1] = x[1] * x[2]
end
assign_operator!(PD, LinearOperator(f!, [id(u)]))

# Assign Dirichlet boundary data (u = 0)
assign_operator!(PD, HomogeneousBoundaryData(u; regions = 1:4))

# Discretize: choose finite element space
FEType = H1Pk{1,2,3} # cubic H1-conforming element with 1 component in 2D
FES = FESpace{FEType}(xgrid)

# Solve the problem
sol = solve!(PD, [FES])

# Plot the solution
using PyPlot
plot(id(u), sol; Plotter = PyPlot)

Citing

If you use ExtendableFEM.jl in your research, please cite this Zenodo record.

License

ExtendableFEM.jl is licensed under the MIT License. See LICENSE for details.