Perfectly Matched Boundary
The Perfectly Matched Boundary is effectively a perfectly matched layer (PML) that is applied to the open boundary without the need to define a domain (a layer in the geometry). The condition automatically applies the PML formulation using the extra dimension functionality of COMSOL Multiphysics.
The Perfectly Matched Boundary condition only exists for the Pressure Acoustics, Frequency Domain interface. For other interfaces use the classical definition and setup for Perfectly Matched Layers (PMLs).
Geometry
Select the Attenuation direction as Radial (the default), Normal, or Custom. For the Radial option enter the Center coordinate r0, that is a coordinate that approximately gives the location of the radiation source. The Radial option works well for most open problems and it will be applicable for most geometries of the radiation boundary. The Normal option will apply the attenuation in the normal direction to the boundary where the condition is applied. In this case the shape of the radiating boundary is important. For the Custom option enter the Custom attenuation direction in the edit fields.
Scaling and Mesh
Select the Coordinate stretching type as Logarithmic, Polynomial (the default), Rational, or User defined.
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For the Polynomial and Rational options, enter the PML scaling factor and the PML scaling curvature parameter. The default values depend on the selected Coordinate stretching type. The settings correspond to the settings entered for the classical Perfectly Matched Layers (PMLs).
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For the Logarithmic option, enter the PML scaling factor and the Real term scaling factor. The logarithmic scaling applies different scaling to the real and imaginary part of the coordinate transform. The imaginary part follows log(1 − ξ) where ξ is the normalized distance in the layer (goes from 0 to 1), this leads to a rational scaling of the Jacobian (see Ref. 74). The real part follows a linear scaling ξ. The PML scaling factor applies to the full scaling function while the Real term scaling factor only applies to the real scaling functions.
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When User defined is selected, choose the functions to be used for the real and imaginary part of the stretching functions, respectively. These should be Functions defined under the Definitions node.
Enter the Number of mesh points, the default depends on the selected Coordinate stretching type. This represents the mesh resolution in the PML along the extra dimension.
Select Use uniform thickness (not selected per default) to enforce an equivalent uniform thickness in the attenuation direction. This option is only available when the Attenuation direction is Radial. If selected a slight gain may be achieved in numerical precision, but the performance/convergence of iterative solvers may be compromised. For spherical geometries this will make the attenuation behave as a PML with the same settings and a uniform mesh.
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Piezoacoustic Transducer. Application Library path Acoustics_Module/Piezoelectric_Devices/piezoacoustic_transducer
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Acoustic Scattering off an Ellipsoid. Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/acoustic_scattering
Boundary conditions that intersect a Perfectly Matched Boundary are not continued/extended through the boundary. This setup is possible with a classical PML where, for example, an interior wall, a periodic, or an impedance condition can be defined inside the layer. This fact puts some restrictions on the general use of the Perfectly Matched Boundary.