\(\nabla\) Engineering & Mathematics

This is a fantastic open source software that has grown and matured through the years.

It is the equivalent of MatLab. Though sometimes slight changes (usually when using packages) might be required, scripts that works for Octave will also work on MatLab and vice versa.

From version 3.8 it integrates a GUI as well.

Available for Windows, Mac and Linux.

GNU Octave official website

Octave forum

Notes on version 4.0

• On Windows some packages will not install, an example is Symbolic

Another great peace of software. This is a SPICE (Simulation Program with Integrated Circuit Emphasis) simulator taken to the edge.

It is not open source but it is free and it has no limitation at all, just the resources available from your machine :).

Binaries available for Windows and Mac.

It is very well supported, you can find the official user group here

Official LTspice IV website

This is a 1D multi-physics simulator with a graphic interface similar to Simulink.

OpenModelica is based on Modelica, a free open language for modelling of complex physical systems. It supports acausal modelling, ODE and DAE problems.

Acausality is one of the most interesting characteristics of this language. To simulate a model you only need to write the system of equations that defines it, the explicit solution for it will be then found by the solver. This is the main difference between acausal and casual (for example: classic Simulink) approach.

Also, Modelica specify 3D animation for mechanical components, this is very useful for multi-body simulation. Unfortunately at the moment this feature is only well supported by commercial softwares like Dymola

Open Modelica official website.

Open Modelica forum.

This is the way to go if you are looking for an open source symbolic manipulator.

To be precise, wxMaxima is the graphical user interface for Maxima which is the real application.

It is important to note that Maxima can handle numerical expressions as well.

Binaries available for Windows Linux and Mac.

wxMaxima official website

This is an open source 3D multi-physics FEM solver.

Elmer comprises a GUI that allows to mesh and configure boundary conditions and solver. Mesh generation is supported through plugins for Tetgen, Netgen and ElmerGrid

It is important to note that the GUI does not give access to all solvers' features which are available through scripts. However these options are quite esoteric and represent a small set.

A good choice for meshing can also be an external mesher like Gmsh which doesn't need to be compiled as Tetgen and compared to Netgen it is supported through binaries for Windows, Mac and Linux. Also, Gmsh binaries support STEP and IGES while Netgen needs to be recompiled (on any platform) with OPEN CASCADE to do so.

The post-processing is usually performed by other applications, for example Paraview, VisIt or Gmsh.

Binaries are available for Windows and Linux. On Mac (and any other environment) it will run through a VM which is officially supported as well.

Elmer official website

Elmer official forum

This is an open source 3D modeller, it is young (at the moment in V0.15) but already capable. Those of you that have used CATIA will find some of its features familiar. Available for Windows, Mac and Linux.

FreeCAD official website