This is a quick implementation of a simple Finite Element (FE) solver using Eigen for the computations and Qt the for the graphical user interface (GUI).

This code solves the magnetostatic Poisson problem with the Finite Element Method on a two-dimensional triangular mesh. The mesh file is imported from Gmsh. The user defines the material parameters and excitation for each Physical region using the GUI. Zero Dirichlet condition is assumed on all Physical Lines.

The GUI visualizes the solutions with contour plots. Since the main purpose of the code (for the author) is to play with visualizations, the solution is recomputed every time the material parameters is changed.

Technical details:

Mesh files generated with GMsh are imported with mesh.cc, mesh_element.cc, mesh_file.cc and mesh.cc. Material parameters are specified with Region- objects and assembled into a map according to the "physical numbers" (see region.cc and region.h). The element stiffness and mass matrices for first order basis functions are computed with Gaussian quadrature and assembled into global stiffness and mass matrices in element.cc and assembly.cc.

Sparse LU solver of Eigen is used for the solution of the resulting system of equations. This code is applicable to large problems even with ~1M degrees of freedom.

The GUI is implemented with Qt in meshplot.cpp, physlist.cpp, mainwindow.cpp and main.cpp:

• Files meshplot.cpp and meshplot.h implement a QWidget for visualizing geometric primitives such as lines and polygons with QPainter.
• Files physlist.cpp and physlist.h implement a QWidget based on QTableWidget for the mainpulation of material parameters and source currents.