Python notebooks that illustrate some pattern formation models (mostly on triangular meshes and without periodic boundaries).
fem_brus_circle.ipynb : Brusselator reaction diffusion equation on a triangular mesh of a circle. The boundary condition is Neumann with both fields having normal component of gradient equal to zero. The system is integrated with the scikit-fem finite element package. fem_complex_ginzburg_landau.ipynb: Integrating the Complex Ginzburg Landau equation on a triangular mesh of a circle with the Neumann boundary condition.fem_swift_hohenberg.ipynb: Integrating the Swift-Hohenberg model on a triangular mesh of a circle with the natural boundary conditions. We use a Morley element because the Swift-Hohenberg model contains 4-th order derivatives (the biharmonic operator).
square_react_diff.ipynb: Conventional periodic boundary conditions on a Cartesian grid integration of Reaction diffusion equations.
square_swift_hohenberg.ipynb: Spectral method on a Cartesian grid integration of the Swift-Hohenberg equation.
fem_loop.ipynb: Wave and heat equation on a periodic 1d boundary with skfem
fem_square_Laplace.ipynb Solving Laplace's equation on the unit square with a mix of non-zero Neumann and Dirichlet boundary conditions.
fem_brus_circle_nonzeroneumann.ipynb Brusselator model with a non-zero Neuman boundary condition. I also include an example with parts of the boundary satisfying Dirichlet and parts of the boundary satisfying Neumann conditions. This uses skfem and a triangular mesh of the circle.
fem_GS_circle_nonzeroneumann.ipynb Gray scott model with a non-zero Neuman boundary condition. I also include an example with parts of the boundary satisfying Dirichlet and parts of the boundary satisfying Neumann conditions. This uses skfem and a triangular mesh of the circle.
Bruss_Var_Mesh.ipynb Solving the Brusselator and Gray-Scott pattern formation model on different shaped 2D domains using pygmsh generated meshes and natural boundary conditions. This uses pacakges skfem and pygmsh
fem_complex_ginzburg_landau_var.ipynb Solving the Complex Ginzburg Landau model pattern formation model on different shaped 2D domains using pygmsh generated meshes and different boundary conditions. This uses pacakges skfem and pygmsh
