3.8.3 Perfectly matched layers

Product: Abaqus/Standard  

Elements tested

AC1D2    AC1D3    AC2D4    AC3D8    AC3D20   

Feature tested

This section provides basic verification tests for the perfectly matched layer elements that are used in Abaqus/Standard to truncate the acoustic infinite domain in a direct-solution steady-state dynamic analysis.

Problem description

The simple one-dimensional steady-state acoustic problem on the domain –1 to is solved using different acoustic elements. A source is applied at of the form , where k is the wave number. The perfectly matched layer region is defined from 0 to 0.2 to truncate the domain. The perfectly matched layer coefficient that is used is 250. The wave number is k = 12, which gives the frequency of interest as 19.0986. The density of the acoustic medium is defined as 1, and the bulk modulus of the medium is 100. The source can be interpreted as an acoustic pressure boundary condition of 0.843853958 on the real part and –0.536572918 on the imaginary part. The end of the perfectly matched layer domain has a zero pressure boundary condition on both the real and imaginary parts.

Results and discussion

The analytical solution for this problem is given by . The analytical solution and the solution computed by Abaqus/Standard are in good agreement.

Input files