FEM modeling: Comsol Multiphysics and Elmer.The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for differential equations. It uses variational methods to minimize an error function and produce a stable solution. Analogous to the idea that connecting many tiny straight lines can approximate a larger circle, FEM encompasses all the methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain. Here Comsol Multiphysics (commercial) and Elmer (open source) software packages are briefly discussed that are used for modeling/solving physical and engineering problems treatable by FEM. Comsol MultiphysicsCOMSOL Multiphysics is a finite element analysis, solver and Simulation software / FEA Software package for various physics and engineering applications, especially coupled phenomena, or multiphysics. COMSOL Multiphysics also offers an extensive interface to MATLAB (hence, also Octave) and its toolboxes for a large variety of programming, preprocessing and postprocessing possibilities. The packages are crossplatform (Windows, Mac, Linux). In addition to conventional physicsbased user interfaces, COMSOL Multiphysics also allows for entering coupled systems of partial differential equations (PDEs). The official site of the software owner is comsol.com A few presentations on modeling with Comsol:
ElmerElmer is computational tool for multiphysics problems. It has been developed by CSC  IT Center for Science in collaboration with Finnish universities, research laboratories and industry. Elmer FEM solver is free and opensource software, subject to the requirements of the GNU General Public License (GPL). Elmer includes physical models of fluid dynamics, structural mechanics, electromagnetics, heat transfer and acoustics, for example. These are described by partial differential equations which Elmer solves by the Finite Element Method. Elmer comprises several different parts: The boundary conditions and physical models are defined in ElmerGUI. The resulting problem definition is solved by ElmerSolver. Finally the results are visualized by ElmerPost. Additionally a utility ElmerGrid may be used for simple mesh manipulation. The different parts of Elmer software may also be used independently. The strongest of the components is ElmerSolver which includes many sophisticated features. For pre and postprocessing other alternatives are available around. The software runs on Unix and Windows platforms and can be compiled on a large variety of compilers. The solver can also be used in parallel mode on platforms that support MPI. The official site of the software is www.csc.fi/elmer
