Perfectly Matched Layer
A Perfectly Matched Layer node () applies a complex coordinate scaling to a layer of virtual domains surrounding the physical region of interest. When appropriately tuned, this layer absorbs all outgoing wave energy in frequency-domain problems, without any impedance mismatch causing spurious reflections at the boundary.
To add a Perfectly Matched Layer to any Component, click Perfectly Matched Layer in the Definitions toolbar, or right-click the Definitions node under the Component and choose Perfectly Matched Layer. If the nodes under the Component node are grouped by type, you can instead right-click Artificial Domains under Definitions.
Settings
The Label is the default perfectly matched layer name.
The default Name (for the first perfectly matched layer in the model) is pml. The Name provides a namespace for variables created by the Perfectly Matched Layer node. For example, the scaled x coordinate can typically be accessed in equations and postprocessing as pml1.x. See the Equation View subnode for a complete list of available variables.
To display the Equation View node under all nodes creating variables, click the Show More Options button () and select Equation View in the Show More Options dialog box. See also Equation View.
Domain Selection
Select a set of domains conforming to the selected geometry type. See Standard Geometry Configurations.
Geometry
Select a Type: Cartesian (the default), Spherical, Cylindrical, or User defined.
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If Spherical is selected, enter the position of the center of the spherical geometry in the Center coordinate table. For axisymmetric models, only the z coordinate is required since the geometry must be centered on the axis.
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If Cylindrical is selected, enter the position of a point on the cylinder axis in the Center coordinate table. For 3D models, also enter a Center axis direction vector.
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If User defined is selected, first choose the Number of stretching directions appropriate for the geometrical configuration. Then for each stretching direction specify a Distance function, evaluating to the distance from the inner boundary of the PML measured in the stretching direction, and the Thickness of the PML in the same direction.
Each of these types (except the user-defined type) requires certain geometrical configurations and not all of them are available for all space dimensions.
Scaling
Select a Coordinate stretching type: Polynomial (the default), Rational, or User defined. See PML Implementation for help on making a decision.
Select an option from the Typical wavelength from list: Physics interface (the default) or User defined. If Physics interface is selected, select one of the interfaces supporting PMLs from the Physics list. If User defined is selected, enter a value or expression for the Typical wavelength. The default is 1.
The Physics interface setting has no effect in Eigenfrequency studies. In that case, the typical wavelength is redefined to be equal to the PML width, as drawn in the geometry. The User defined option applies unaltered.
When using the PML in the Pressure Acoustics, Transient interface, then if you change the Typical wavelength from option to User defined, it is not the actual wavelength that should be entered but rather the speed of sound per Hertz. For example, if User defined is selected in a normal air domain, then enter 343[m/s]/1[Hz]. The reason is that in the time domain the PML formulation is not related to wavelength but to speed of sound. Transient signals typically include many Fourier frequency components. For the implementation related to the time domain see the Theory for the Perfectly Matched Layers in the Time Domain section in the Acoustic Module User’s Guide.
For the predefined Polynomial and Rational stretching types, enter a value or expression for the PML scaling factor and the PML scaling curvature parameter which can be used to tune the PMLs for wave fields with evanescent components or wavelengths deviating from the free-space wavelength of plane waves. See further PML Implementation. The defaults are 1 for both.
For the User defined stretching type, select Real part of stretching function and Imaginary part of stretching function from functions defined under Global>Definitions or under Definitions in a component, or leave the default value None, which for the real part is interpreted as f(ξ) = ξ and for the imaginary part as f(ξ) = 0. Any function node defining a single function of one or two arguments is eligible for use as a stretching function. The first argument is interpreted as a dimensionless distance, ξ, in the range 0 to 1, and the second argument — if present — as the typical wavelength.
If you have the Acoustics Module, see these examples:
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Cylindrical Subwoofer: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/cylindrical_subwoofer
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Acoustic Scattering off an Ellipsoid: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/acoustic_scattering
If you have the RF Module, see these examples:
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2D, cylindrical PML — Radar Cross Section: Application Library path RF_Module/Scattering_and_RCS/radar_cross_section
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3D, spherical PML with swept mesh —RF Coil: Application Library path RF_Module/Passive_Devices/rf_coil