The finite element method (FEM) is a numerical technique for finding approximate solutions to equilibrium or boundary value 

problems, eigenvalue problems, propagation or initial value problems for partial differential equations. Difference of FEM with other numerical methodology (especially Finite differential method, FDM) is subdividing a domain into elements. Element can become any shape and size. So it is possible to fill boundary with elements in spite of strange shape of boundary.

This process needs mesh generation. There are many open source mesh generator and they operates like this image.Generally, triangle (2D) or tetrahedron (3D) shape is used for subdividing domain.

 FEM is nowadays widely used by these properties. And finite element method include variational formulation. Galerkin method is widely used out of the others because it is most common. 

2. Quantum Transport Simulation

Quantum transport simulation is performed to obtain I-V characteristics (or mobility sometimes) of target device. For quantum transport simulation, first of all, Hamiltonian should be constructed. In our laboratory, Hamiltonian is   obtained by using atomistic level approaches. By using the Hamiltonian, band structure of channel material can also be obtained. Current and charge density are obtained by self-consistently solving non-equilibrium Green function (NEGF) and Poisson equation. We develop quantum simulator employing flow above. We also analyze device characteristics by using simulation results.