Learning the Finite Element Method with MATLAB and GID


Many problems related to steady-state oscillations (mechanical, acoustical, thermal and electromagnetic) lead to the two-dimensional Helmholtz equation
(∇^2+k^2 )u=0

This equation is a time-independent linear partial differential equation. The interpretation of the unknown u and the parameter k depends on what the equation models. The most common areas are wave propagation problems and quantum mechanics, in which case u is the amplitude of a time-harmonic wave and the orbitals for an energy state, respectively.

This equation is solved with the FEM in order to show the application of the method in other fields.