Elmer for PDEs

Elmer is an open-source multiphysics simulation software that has been around since 1995. It is developed by the CSC — IT Center for Science Ltd. This group is administered by the Ministry of Education, Science and Culture in Finland. With Elmer, you can model physical systems, such as fluid dynamics, electromagnetism, heat transfer and acoustics. All of those problem areas have one thing in common—they are all described by partial differential equations (PDEs).

A PDE is a differential equation that depends on more than one variable, usually more than one space variable. For example, an equation that describes how heat gets transferred across a metal plate, where a is the thermal diffusivity of the metal plate, would look like the formula shown in Figure 1.

Figure 1. Sample Equation

Very simple PDEs have exact solutions, but anything more complex that describes more physical situations just can't be solved exactly. This is where numerical solutions come into play. There are three widely used methods: finite element, finite volume and finite difference methods. Elmer uses the finite element method. The basic idea is to break up the problem space into some kind of a mesh of smaller spaces, and then either eliminate the PDE completely, by reworking it into a steady state problem on the mesh, or approximating the PDE with a system of ordinary differential equations that then are integrated using standard methods, like Euler's method or Runge-Kutta.

Elmer is distributed under the GPL, so you always can download the source and compile your very own version. Binaries are available for all those poor users still stuck on Windows. Packages should be available for most Linux distributions. For Ubuntu-based distros, you simply can use the following to install Elmer and all the necessary libraries:

sudo apt-get install elmer

Elmer is broken into several parts. ElmerSolver is the part that actually takes the input files and does the calculations to evolve the PDE you are interested in. ElmerPost is the visualization and post-processing tool. With this tool, you actually can see the results of your calculations. ElmerGrid is the meshing tool that can create simple 1-D, 2-D and 3-D meshes that will be used to evolve your PDE. It also can be used to import meshes generated using other software packages, such as those created using the Ansys tools.

There also is a GUI interface called ElmerGUI. ElmerGUI allows you to define and generate input files for ElmerSolver, as well as import external meshes from other software (Figure 2).

Figure 2. ElmerGUI

Looking at all of this, you may be thinking, "This is perfect!" So, I also should mention some of Elmer's downsides. Elmer actually is a suite of tools, and those tools are not always at the same development level. The documentation tends to lag behind the newest features, and ElmerGUI may be missing some of the more esoteric methods and models that ElmerSolver can use. Elmer is a huge system, and like any large software package, it has a steep learning curve. The tools available (ElmerGrid) can handle generating only relatively simple meshes. This means that if you have a very complicated system, you likely will need to use some other tool to generate the mesh and then import it into Elmer. If you can work around these possible deficiencies, Elmer may be exactly the right solution for you.

ElmerGUI is likely to be what most people prefer using. You can import element mesh files in various formats, generate element partitionings for geometry input files, set up the PDE systems you want to solve, and export model data to hand in to ElmerSolver. Most conveniently, ElmerGui also provides an interface to the parallel version of the solver, ElmerSolver.mpi. There also is a built-in post-processor that allows you to view your results right there from ElmerGUI. The menus in ElmerGUI are fully programmable as well, so you can tune the interface to match your specific problem area better.