FerriteInterfaceElements.jl

Welcome to the documentation for FerriteInterfaceElements! FerriteInterfaceElements adds functionality to the finite element toolbox Ferrite for working with interface elements (also known as cohesive elements).

How the documentation is organized

The documentation assumes that you are already familiar with the basic usage of Ferrite. If not, you should first take a look at the Ferrite documentation. Here, only the additional tools are explained.

After a basic introduction on this side, the document is organized as follows:

• Tutorials are documented examples which guide you through the process of solving partial differential equations with interface terms.
• Reference contains the technical API reference of functions and methods (e.g. the documentation strings).

Getting started

As a new user of FerriteInterfaceElements it is suggested to read the introduction on this side and then start working with the tutorials before using FerriteInterfaceElements to tackle the specific equation you ultimately want to solve.

Getting help

If you have questions about FerriteInterfaceElements it is suggested to use the #ferrite-fem channel on the Julia Slack, or the #Ferrite.jl stream on Zulip. Alternatively you can use the discussion forum on the GitHub repository.

Installation

To use FerriteInterfaceElements you first need to install Julia, see https://julialang.org/ for details. Installing FerriteInterfaceElements can then be done from the Pkg REPL; press ] at the julia> promp to enter pkg> mode:

pkg> add FerriteInterfaceElements

This will install FerriteInterfaceElements and all necessary dependencies. Press backspace to get back to the julia> prompt. (See the documentation for Pkg, Julia's package manager, for more help regarding package installation and project management.)

Note, that you also need to install Ferrite, which can be done in the same way.

Finally, to load Ferrite and FerriteInterfaceElements, use

using Ferrite, FerriteInterfaceElements

You are now all set to start using FerriteInterfaceElements!

Introduction to interface elements

Interface elements can be used to allow for jumps in fields on interfaces between finite elements. They can be considered as elements with zero thickness and two faces (one for each side of the interface).

In FerriteInterfaceElements, their implementation is based on the idea to combine two embedded elements to represent the to sides of an interface. At the current state, it is only supported to use the same interpolation on both sides. To distinguish the two sides, they are referred to as here and there. The jump of a field is then defined as from here to there: field there - field here.

Another key definition is the reference shape of interface elements. In FerriteInterfaceElements, the shape is chosen to be of the same dimension as the surrounding bulk elements. The specific shape is then determined from the shape of the underlying base shapes:

These definitions have been made to use as much of the existing functionalities in Ferrite as possible on the types for working with interface elements:

• InterfaceCell
• InterfaceCellInterpolation
• InterfaceCellValues

These types can be used similar to the corresponding types in Ferrite. However, they come with new functions for evaluations:

• getdetJdV_average
• shape_value_jump
• shape_value_average
• function_value_jump
• ...