Exterior Field Calculation

Use the 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 used in subsequent postprocessing. Here the feature allows the calculation and visualization of the pressure field outside the computational domain at any distance including amplitude and phase. 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. 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. If an interior boundary is used, the material properties should be continuous across 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).

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.

Enter an for the exterior field acoustic pressure field (the default is pext).

If required, 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 and 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: (the default), , or . 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.

When one of the 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 section by clearing the check box .

Select a : (the default) to compute The Helmholtz-Kirchhoff Integral Representation or the → ∞ to compute the value in The Far-Field Limit.


	The exterior field pressure is evaluated using the exterior field operator (the name is defined in the Exterior field variable name input field, the default is pext). 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 older versions of COMSOL Multiphysics the Exterior Field Calculating feature was called Far-Field Calculation. The Exterior Field Calculating has an improved GUI and uses the full integral as default. In acoustics the amplitude and phase of the pressure signal are in most cases necessary and evaluation is often not performed in the true far field (beyond the Rayleigh radius of radiating bodies).

Advanced Settings

To display this section, click the button (

) and select .

The option 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. In these cases, use a single boundary layer mesh on the inside of the outer boundary or on the inside of the PML to enhance the precision of the exterior field calculation.

The option 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.

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Evaluating the Acoustic Field in the Exterior: Near- and Far-Field

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Several dedicated acoustics plots rely on the exterior field calculation, see Dedicated Acoustics Plots for Postprocessing

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ppr and pprint and up and down (operators) in the COMSOL Multiphysics Reference Manual

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Acoustic Scattering off an Ellipsoid: Application Library path