fenics-demo-uop

Setup

• First, install key packages following setup/essential_packages.md

• Next, follow instructions in setup/conda_and_fenics_setup.md to install conda and fenics and test fenics code.

Examples

1. Meshing Examples File shows examples of creating meshes using either gmsh or pygmsh python package. File also shows how to create .geo file for complex geometries and run gmsh code in python. If it is a 2-d mesh, you can also easily plot the mesh using dolfin plot function.

   File in folder meshing_using_pygmsh uses pygmsh to create the mesh (i.e., it bypasses creating a .geo file). Mesh of standard geometries are implemented. For most of the geometries when possible one can create a symmetric mesh by creating the mesh of one part of the domain and mirroring it.

2. fenics_examples Fenics (2019.1.0) implementation. Examples include:

   1. Poisson Equation We solve Poisson equation in 2-d in simple and complex geometries. This jupyter notebook file is also a good starting example of using notebook to seamlessly combine markdown text, python codes, and output of codes.

   2. Nonlinear Poisson Equation Nonlinear version of Poisson equation is used to show how nonlinear variational problems can be solved in Fenics. Newton and Picard iteration methods are explained and implemented and compared with the Fenics's solve method for nonlinear variational problems.

   3. Elasticity - material deformation in 2-d and 3-d We consider three different models (or constitutive relations and small/large deformation theories) of beams subjected to twisting and bending loading: isotropic linear elastic beam, orthotropic linear elastic beam, and beam made of hyperealstic material with large deformation theory.

3. fenicsx_examples Fenicsx implementation. Examples include:

   1. Elasticity - material deformation in 2-d and 3-d Fenicsx implementation of fenics_examples/elasticity/elasticity.ipynb.