The development of computers creates an opportunity to develop methods for creating high accuracy model of the acoustic space. One common method use for this is the Finite Element Method (FEM). The time dependent finite element method allows us to simulate the physical space in discrete time when the time-harmonic analysis would be difficult.
The disadvantage of the finite element method is that it only provide appropriate model in radiation problems with some extensions. One of this the Perfectly Matched Layer (PML). When using the PML we create anisotropic absorbing layer around the physical domain at the radiation. The incident wave at the inner surface of the PML does not make any reflection and in the layer they are damping. The reflection from the outer boundary of the PML (with carefully chosen parameters) will not make significant error.
In this paper we describe the formulation of the finite element method and two of its time domain solutions. We discuss the advantages and disadvantages of these solutions over the one and two-dimensional waveguide models with simulations in MATLAB.
After we show the formulation of the time-dependent PML. We test the PML in the one and two-dimensional waveguide models, and discuss its errors.