Three-dimensional finite element time domain methods

The finite element time domain (FETD) method in three dimensions with nodal elements is formulated. The method is applied to the scattering of a Gaussian pulse by a dielectric sphere and the frequency domain results are obtained by using discrete Fourier transform. It is shown that while the uniaxial perfectly matched layer (UPML) is suitable as an absorbing boundary condition for the finite difference time domain (FDTD) method and for the FETD with edge elements, in the case of nodal elements it is necessary to use the original Berenger's perfectly matched layer (PML). The reason is that PML and UPML differ in the divergence property of the electric field.; FETD with nodal elements, FETD with edge elements and FDTD are compared and their important characteristics are verified. It is shown in a new way that FDTD is a special case of FETD with edge elements when rectangular brick elements with linear interpolation functions are employed.