Exterior Field Calculation
Use the Exterior Field Calculation node to apply the source boundaries for the exterior field transformation set up by the Helmholtz-Kirchhoff integral. You also specify a name for the acoustic exterior field variable (default name is pext) used in subsequent postprocessing. The feature allows the calculation and visualization of the pressure field outside the computational domain at any distance including amplitude and phase. Note that when a Background Pressure Field is present, the feature only operates on the scattered field variables and is thus also well suited for analyzing the results of a scattering problem.
The exterior field boundary should be continuous and needs to enclose all sources and scatterers with the desired symmetry types (see below). The feature should be applied on an exterior boundary, a boundary on the inside of a PML, or an interior boundary where the normal direction is continuous along the boundary. In the latter case, the advanced physics option Reverse normal direction check box should be marked if the normal is pointing inward (see below). Note also that if an interior boundary is used, the material properties should be continuous across the boundary.
On exterior radiation boundaries and on the inside boundary of a PML the normals are always automatically adjusted. In all other cases the direction of the normals can be visualized with an arrow surface or line plot in postprocessing, plotting nx, ny, and nz.
 
For gradient based optimization a dedicated operator exists in 3D (only for the Symmetry plane option) for the pressure pext_opt(x,y,z) and for the sound pressure level Lp_pext_opt(x,y,z). These two operators can be used to define objective functions, like specifying a target spatial response.
An example is given in the Shape Optimization of a Rectangular Loudspeaker Horn in 3D tutorial. Application Library path Acoustics_Module/Optimization/rectangular_horn_shape_optimization
Exterior Field Calculation
Enter an Exterior field variable name for the exterior field acoustic pressure field (the default is pext).
Select the Symmetry type that applies to the problem. The symmetry type and subsequent settings should match the conditions used in the underlying acoustics problem, for example, if using Symmetry or the Periodic Condition.
Select Symmetry planes (the default), Sector symmetry, or Sector symmetry with one symmetry plane:
For Symmetry planes, if no symmetry conditions are used (the default) the exterior field feature boundaries should form a fully closed surface. If necessary, select and add a condition for one of the Cartesian coordinate planes (with a possible offset) to model either a symmetry condition in the plane (which is the same as an infinite sound hard boundary) or an antisymmetry condition in the plane (which is the same as an infinite sound soft boundary). The infinite sound hard boundary option is especially useful when modeling system with an infinite baffle configuration.
For each of these planes, select the type for the condition to be applied in the x = x0, y = y0, or z = z0 planes. Select the type of condition: Off (the default), Symmetry/Infinite sound hard boundary, or Antisymmetric/Infinite sound soft boundary. Then enter the value for the plane location x0, y0, or z0 (the default is 0 m). This allows an offset of the infinite condition planes along the main coordinate axes.
The Sector symmetry options allows the underlying geometry to represent only a sector (an subdivision of a full 360o rotation). Select and define the properties of the sector. First select the Transformation applied to the sector, either Rotation (the default) or Reflection and rotation. For the latter enter the Reflection plane used for the initial reflection of the sector. The selection is restricted to the main coordinate planes (move and rotate the geometry if necessary). The offset distance (x0, y0, z0) is given by the point a0. Enter the coordinates for the Point on sector symmetry axis, a0 as well as the Sector symmetry axis direction, adir (default is adir = (0, 0, 1)). Enter the Number of sectors n, which has to be an integer and for the Reflection and rotation option an even integer. Finally, if the pure Rotation option is selected enter an optional Azimuthal mode number m (the default it 0). This option is typically only relevant when used together with Periodic Condition.
Note that the Sector symmetry option cannot be combined with an infinite baffle (symmetry plane) used in many transducer models. For this type of setup use the Sector symmetry with one symmetry plane option.
The Sector symmetry with one symmetry plane option allows for the combination of sector symmetry and a single symmetry plane, under certain restrictions. First, select the single Symmetry plane and symmetry Condition. The offset distance (x0, y0, z0) is given by the point a0. Then follow the same settings as for the Sector symmetry option. Note that the sector symmetry axis direction adir is automatically defined as being normal to the single symmetry plane.
When one of the symmetry plane conditions is enabled the infinite plane, where it applies, is rendered and can be visualized in the Graphics window. This rendering can be turned off in the Physics Symbol section by clearing the check box Show physics symbols.
Select a Type of integral: Full integral (the default) to compute The Helmholtz-Kirchhoff Integral Representation or the Far-field integral approximation for r → ∞ to compute the value in The Far-Field Limit.
To evaluate the pressure in a point (x0,y0,z0), simply write pext(x0,y0,z0). To evaluate the sound pressure level in the same point, it is advantageous to use the subst() operator and write, for example, subst(acpr.efc1.Lp_pext,x,x0,y,y0,z,z0).
An example of this is given in the Loudspeaker Driver — Frequency-Domain Analysis tutorial model from the Acoustics Application Libraries.
In 2D axisymmetry the evaluation of the exterior-field integral automatically includes the Azimuthal mode number m from the Pressure Acoustics Equation Settings. For postprocessing purposes, for example in a Radiation Pattern plot, it is necessary to include the azimuthal component explicitly by writing: pext(r,z)*exp(-i*acpr.m*phi).
Advanced Settings
To display this section, click the Show More Options button () and select Advanced Physics Options.
The option Use polynomial-preserving recovery for the normal gradient on interior boundaries is selected per default on interior boundaries. This means that the exterior field feature automatically uses the polynomial-preserving recovery operator ppr() to get an enhanced evaluation of the normal derivative of the pressure. This increases the precision of the exterior field calculation. If you click to clear this check box this removes all instances of the operator from the equations.
The ppr() operator is not added when the exterior field calculation is performed on an external boundary or a boundary adjacent to a perfectly matched layer (PML) domain. In the latter case, the down() or up() operator is automatically added in order to retrieve values of variables from the physical domain only.
The option Reverse normal direction on interior boundaries allows reversing the normal used in the Helmholtz-Kirchhoff integral. To get the correct phase the normal has to point inward. Typically, if the exterior field is calculated in an interior boundary to the physics (not a boundary next to a PML), the normals will point outward and the option should be used.
ppr and pprint and up and down (operators) in the COMSOL Multiphysics Reference Manual
Acoustic Scattering off an Ellipsoid. The Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/acoustic_scattering