## Studies and Solvers

### Store Selected Parts of a Solution

When running studies in COMSOL Multiphysics version 5.2, you can store selected parts of your solution. This saves memory and computing power when you only need part of the solution for visualization and results.

Use this new functionality with the following steps:

- Create one or several named selections (Component > Definitions > Selections).
- Select your named selections in the drop-down menu in the
*Values of Dependent Variables*section of any standard study step.

*This example model shows how an object is detected by radar, using perfectly matched layers to absorb outgoing waves without reflecting them. With this new functionality, you can discard the solution in the perfectly matched layer and only store the solution in the space surrounding the boat, reducing the size of the solution from 184 MB to 142 MB. Size reduction can be even more significant for certain models.*

### Two New Runge-Kutta Solvers

There are two new explicit Runge-Kutta solvers, RK34 and Cash-Karp (RK45). RK34 combines adaptivity with good stability properties along the imaginary axis, suitable for oscillatory problems. Cash-Karp is similar to the Dormand-Prince 5 solver (added with an earlier version of the software), but has an even larger stability region along the negative real axis, which is more efficient for naturally damped problems. Both of the new solvers come with state-of-the-art adaptivity through a PI control strategy, stiffness detection, and a novel technique to determine the initial time step.

### Enhanced FFT Studies and Solvers

COMSOL Multiphysics version 5.2 greatly extends the functionality of the fast Fourier transform (FFT) study steps, which include Time to Frequency FFT, Frequency to Time FFT, and the corresponding FFT solver.

The *input time* range for the Time to Frequency FFT (forward FFT) study step is now specified by a start time and end time instead of a time list. The number of interpolated input solutions, N, is derived from the specified maximum output frequency (the derived value of N is shown in the solver log). Two variants are available for scaling the solution: discrete scaling (unscaled) and continuous scaling (scaled by the time or frequency step). Additional choices for window functions include Rectangular, Gaussian, Hamming, Hanning, Blackman, and Tukey. These functions are located above the From expression and *Cut-off* options.

The *Do not store negative frequencies for real input* option for Time to Frequency FFT (forward FFT) removes redundant information in the complex output data for real input data. For the Frequency to Time FFT (inverse FFT) study step, the input data for given nonnegative or nonpositive frequencies is, by default, extended by negative frequencies or positive frequencies with complex-conjugated input values. This default can be switched off at the solver level with the option *Extend input samples* using two choices: *Add complex conjugate pairs* (default) and *Use original data. Extend input samples* enables you to create real output data from complex input data, which basically recreates the data removed by the *Do not store negative frequencies for real input* option for the Time to Frequency FFT.

For the Frequency to Time FFT, there is an *Add stationary solution* solution selector to extend the input data for frequency 0. This is done by a stationary solution that is either taken as the data for frequency 0, or added to the data for frequency 0.

The *output timelist* for Frequency to Time FFT now corresponds precisely with the set of output time values computed (i.e., the output time values specified). The number of output solutions can be different from the number of input solutions. Compared to earlier versions of the software, there is no longer any cutoff or padding of the output solution to meet a full period or artificial output step size (overruling the specified size).

The *Periodic input data* option is no longer available at the study level. At the solver level, this option is always available for the forward and inverse transformations if the *Extend input samples* selector is set to *Use original data* (the nondefault option). If *Periodic input data* is checked, the periodic value is no longer appended to the end of the output data, which created the same number of inputs and outputs in earlier versions of COMSOL Multiphysics.

The selector for the transformation algorithm for inverse transformation (e.g., Automatic, Fast Fourier transform, or Nonuniform Fourier transform) is no longer available. The FFT algorithm is only applied for the inverse transformation if the output time list is equidistant and the given output time range matches the input data. The functionality of the FFT study steps is now based on the Intel® Math Kernel Library (MKL).