An alternative method to simulate the pressure wave excited by the analytic incident wave sources (defined using the AWAVE command), is to use scattered pressure as the solved variable. Pure scattered pressure formulation may be used in the following situations:
The scattered pressure is much smaller than the incident pressure wave, and the scattered properties are under the investigation.
The analytic wave sources defined using the AWAVE command are inside the model for real acoustic devices, such as an enclosed-back loudspeaker.
When the scattered pressure is investigated as the degree of freedom, the total pressure is split into incident pressure and scattered pressure. This can be expressed as:
 | (8–156) |
The pressure boundary conditions are also changed for the scattered pressure.
For the Dirichlet boundary (p =p0):
 | (8–157) |
For the Neumann boundary 
:
 | (8–158) |
The boundary of each decomposed domain is assumed to consist of the truncation surface Γext, impedance surface ΓZ, and FSI interface ΓFSI. This can be expressed as:
 | (8–159) |
The "weak" form for the scattered pressure derived from Equation 8–33 is written as:
 | (8–160) |
By decomposing Equation 8–160 into the environment medium (Ω0) and non-environment medium (Ωd), and assuming that the incident pressure wave satisfies the wave equation in the environment medium, we can state that:
 | (8–161) |
The "weak" form of the incident wave including acoustic-structure interaction can be written as:
 | (8–162) |
Substituting Equation 8–160 and Equation 8–162 into Equation 8–33 yields the "weak" form for pure scattered pressure based formulation, expressed as:
 | (8–163) |
By combining the Neumann boundary condition ΓN (expressed in Equation 8–157 ) with Equation 8–163, the matrix form is written as:
 | (8–164) |
where:
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Since the scattered pressure is solved in the acoustic domain and the total pressure is coupled with the structural domain, the total pressure in the structural matrix in Equation 8–142 must be split to ensure a consistent pressure degree of freedom in the solution. This is expressed as:
 | (8–165) |
The coupling matrix equation is given by:
 | (8–166) |
Equation 8–65 is used for the scattered pressure in the PML, because only scattered pressure is absorbed and the incident is assumed to satisfy the wave equation in the environment medium.