A Partial Fraction Fit function () uses a modified adaptive Antoulas–Anderson (AAA) algorithm, AAA2, to compute a partial fractional fit. Use this function for a rational approximation of frequency-domain responses. This approximation makes it possible to compute its inverse Fourier transform analytically and thus obtain the time-domain impulse response function. Doing so is useful in, for example, models using a Pressure Acoustics, Transient or Pressure Acoustics, Time Explicit interface. You select frequency-dependent impedance data as input and can then use the fitted parameters to set up an impedance condition. See the Acoustics Module User’s Guide for more details. The Partial Fraction Fit function is, in general, a complex-valued function of a real-valued argument (frequency). The algorithm treats the input data as complex numbers, not separating its real and imaginary parts.

Select a Data source — File or Result table to define the data source for the partial fraction fit function.

If you select File (the default), enter the complete network path and name of the data file in the Filename field, or click Browse to select a text or data file with spreadsheet data in the Interpolation Data dialog box. The data should contain a column containing frequency values and columns containing real and imaginary value parts. You can import data files with comma-separated, semicolon-separated, space-separated, and tab-separated data. You can also click the downward arrow beside the Browse button and choose Browse From () to open the fullscreen Select File window. Click the downward arrow for the Location menu () to choose Show in Auxiliary Data () to move to the row for this file in the Auxiliary Data window, Copy Location (), and (if you have copied a file location) Paste Location (). Also choose a decimal separator from the Decimal separator list: Point (the default) or Comma. Click Import () to import the data into the model; otherwise, COMSOL Multiphysics references the data on your file system. Click Export to save the data for the partial fraction fit function to a file and reference from there instead of including it in the model. Click the Discard button to delete the imported data for the partial fraction fit function from the model. Click the Refresh button ()to ensure that the file is reread when needed.

If you select Result table, choose the table to use from the Result table list.

In the Data Column Settings section, you specify how each column in the input data, displayed in the Columns column should be interpreted in the Type column — as Frequency, Real, Imaginary, or as an Ignored column — and their units, if applicable, can be entered or selected from the Unit list underneath the table and will appear in the Settings column. The function can only have one Frequency column, one Real column, and one Imaginary column. When you click the Fit Parameters button () at the top of the Settings window, the AAA2 algorithm is run on the input data to make a partial fraction fit, which in turn returns poles, residues, and an asymptotic term. Those are used in an analytic expression that defines the function.

If desired, change the relative tolerance for the partial fraction fit in the Tolerance field (default: 1·10−3). In practice, a higher tolerance results in a greater number of poles and residues and increases the computation time. A too tight tolerance may cause the algorithm to stagnate and yield spurious poles (Froissart doublets).

This section contains the real-valued parameters in the Residue, R and Pole, ξ columns of the table under Real residues and poles and complex-valued parameters in the Residue, Q and Pole, ζ columns of the table under Complex residues and poles. Use the Delete Row () and Clear Table () buttons as desired to edit the tables. Use the Load from File () and Save to File () buttons to load or save data to or from the tables. You can also click the downward arrow beside the Load from File button and choose Load From () to open the fullscreen Select File window.

The asymptotic term, Y∞, appears in the Y∞ field (default: 0).

Sometimes the computed partial fraction fit can have poles with positive real parts. These unstable poles correspond to exponentially growing terms in the time-domain impulse response function. Click the Flip Poles button () to flip the unstable poles to the left half-plane. The residues and the asymptotic term will be updated automatically.

Click the Update Residues button () after you have modified or discarded existing poles or manually added new poles. The residues and the asymptotic term will be updated. This may be useful if, for example, you discard poles, whose contributions are negligible.