What is the difference between Finite Difference (FD) and Finite Element (FE) for wave propagation problems?
Finite Difference methods are a simple and straightforward method of implementing a numerical solution method, however can result in some difficulties in practical use. The element size in the model is fixed across the entire grid, meaning the boundaries of materials can be difficult to place accurately, and excess meshing may be required if certain model components are particularly small. There are also some difficulties in applying boundary conditions in a straightforward manner. While there are potentially some small reductions in efficiency, the versatility offered by Finite element approaches in ensuring the material boundaries are located exactly and that boundary conditions are simply applied, mean FE is a more practical method then FD for most problems.
