Tutorials

Table of Contents

• Fundamentals
• Mesh creation
• Scalar-field problems
• Problems with complex variable fields
• Vector-field problems
• Mixed field problems
• Data driven problems
• Maxwell problems
• Advanced topics

The tutorials contain a number of basic programs that are built on top of each other. Those with the full source code has the following structure

1. Introduction: Problem being solved, mathematical equations and derivations leading to finite element implementation
2. Implementation: Detailed explanation of the source code where tasks are separated in different functions
3. Results: How to run the program, output, visualisation, interpretation and comments, possible extensions.
4. Plain program: Full source code without extended comments

The source code and corresponding binary files of the tutorials are located at the following directories when you install MoFEM with developer version Installation

• Source code: $HOME/mofem_install/mofem-cephas/mofem/users_modules/tutorials
• Binary files (build directory): $HOME/mofem_install/um/build_release/tutorials

Each tutorial in this page includes code name and keywords for quick reference and search within the browser.

Note

You do not need to go through all the tutorials in the order they are listed in this page before jumping into the topic in which you are interested. However, we do recommend you to have a look at the first few tutorials solving scalar-field problems to have a general idea how the finite element implementation is done in MoFEM. We also make a recommendation at the beginning of each tutorial regarding which tutorial(s) you should read (prerequisites) before continuing with the one you are most excited about.

Note

The tutorials are under development. Send us your feedback on Q&A regarding the tutorials that already done and the missing ones that you most prefer to see.

Fundamentals

MoFEM Interfaces	Brief introduction about MoFEM interfaces which enable users to implement the codes with different level of complexity. Keywords:
Hierarchical approximation	Introduce elementary concepts of the Finite Element Method (FEM) with hierarchical shape functions and their implementation in MoFEM Keywords: Hierarchical approximation
fun-0: Hello world	Creating Simple problem, and pushing operators to pipelines Keywords: UDOs, pipelines
fun-1: Integration on finite element mesh	Numerical integration is essential for most of the numerical methods employed to solve partial differential equations (PDEs) Keywords: UDOs and integration

Mesh creation

Create a MoFEM-compatible 2D mesh from Gmsh	This document shows how to create a MoFEM-compatible 2D input mesh from Gmsh Keywords: Gmsh, block definition, config file, read_med
Create a MoFEM-compatible 3D mesh from Gmsh	This document shows how to create a MoFEM-compatible 3D input mesh from Gmsh Keywords: Gmsh, block definition, config file, read_med

Scalar-field problems

SCL-0: Least square approximaton	Solve the least square problem to approximate scalar function Keywords: Simple Interface, KSP solver, mofem_part, mbconvert, 3D extension
SCL-1: Poisson's equation (homogeneous BC)	Solve the Poisson's equation with zero value boundary conditions Keywords: Simple Interface, KSP solver, mofem_part, mbconvert, 3D extension
SCL-2: Poisson's equation (non-homogeneous BC)	An expansion of previous tutorial to cover non-homogeneous (non-zero value) boundary condition of Poisson's equation Keywords: Least square approximation
SCL-3: Poisson's equation (Lagrange multiplier)	Solve the Poisson's equation using Lagrange multiplier for the non-homogeneous boundary condition Keywords: PCFIELDSPLIT block solver
SCL-4: Nonlinear Poisson's equation	Solve nonlinear Poisson's equation using Newton iterative scheme Keywords: SNES solver
SCL-5: Minimal surface equation	A variant of the nonlinear Poisson's equation Keywords: SNES solver
SCL-6: Heat equation	This is the first tutorial to solve a time-dependent problem with first-order time derivative Keywords: TS solver, implicit scheme
SCL-7: Wave equation	Time-dependent problem with second-order time derivative Keywords: TS solver, implicit scheme
SCL-8: Radiation boundary conditions	Nonlinear problem at the boundary Keywords: axisymmetric problem, linearisation

Problems with complex variable fields

CLX-0: Hemholtz problem

Hemholtz problem for acoustics Keywords: Complex variable, Linear Solver </tr

Vector-field problems

VEC-0: Linear elasticity	Linear elastic Keywords: Hooke equation
VEC-1: Eigen elastic	Eigen elastic Keywords: Eigen values, SLEP
VEC-2: Dynamic elastic	Dynamic elastic Keywords: Time dependent problem
VEC-3: Nonlinear dynamic elastic	Nonlinear elastic Keywords:

Mixed field problems

MIX-0: Mix poisson equation

A mixed problem Keywords: H-div space

Data driven problems

DD-0: Tranport data driven

Data driven for transport or heat conduction problems Keywords: Scalar problem

Maxwell problems

MAX-0: Magnetostatics	Magnetostatics Keywords:
MAX-1: Lorenz force	Lorenz force Keywords:

Advanced topics

ADV-0: Plasticity	Plasticity problem Keywords:
ADV-1: Contact problem	Contact problem Keywords: H-curl/H-div space, mix formulations
ADV-2: Fracture	Fracture problem Keywords:
ADV-3: Various fields and finite element spaces	Problem with various fields and finite element spaces Keywords:
ADV-4: Elasticity with spring and rod elements	Problem with mixed dimension (1D, 2D, 3D) Keywords: