A direct time-domain FEM modeling of broadband frequency-dependent   absorption with the presence of matrix fractional power: Model I
  The frequency-dependent attenuation of broadband acoustics is often confronted in many different areas. However, the related time domain simulation is rarely found in literature due to enormous technical difficulty. The currently popular relaxation models with the presence of convolution operation require some material parameters which are not readily available. In this study, three reports are contributed to address broadband ultrasound frequency-dependent absorptions using the readily available empirical parameters. This report is the first in series concerned with developing a direct time domain FEM formulation. The next two reports are about the frequency decomposition model and the fractional derivative model. 
W Chen