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 (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 operator and its associated variables are optimized for use in postprocessing. They cannot be used for gradient based optimization studies, like shape and topology optimization, where the sensitivity is necessary. For gradient based optimization a dedicated operator exists in 3D 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. The operator only exists when the Symmetry type option is set to Symmetry planes (the default), this is in particular true when all symmetry planes are set to Off. 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

Select the 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.

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For , 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: (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.

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The 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 applied to the sector, either (the default) or . For the latter enter the 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 , a0 as well as the , adir (default is adir = (0, 0, 1)). Enter the n, which has to be an integer and for the option an even integer. Finally, if the pure option is selected enter an optional m (the default it 0). This option is typically only relevant when used together with Periodic Condition.

Note that the option cannot be combined with an infinite baffle (symmetry plane) used in many transducer models. For this type of setup use the option.

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The option allows for the combination of sector symmetry and a single symmetry plane, under certain restrictions. First, select the single and symmetry . The offset distance (x0, y0, z0) is given by the point a0. Then follow the same settings as for the option. Note that the sector symmetry axis direction adir is automatically defined as being normal to the single symmetry plane.

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.

	If the subst() operator and the exterior field operator pext() are used together, you should never use the frame coordinates as arguments. Instead use dummy variables and write, for example: subst(pext(a,b,c),a,0[m],b,0[m],c,1[m]) Never use x, y, and z in this type of expressions.

	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(-iacpr.m*phi).

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. Note that this layer is automatically added when using the Physics-Controlled Mesh for Pressure Acoustics.

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.