# Frequency Grids¶

GYRE searches for sign changes of the discriminant function $$\Dfunc(\omega)$$ on a grid $$\{\omega_{1},\omega_{2},\ldots,\omega_{M}\}$$ in the dimensionless frequency $$\omega \equiv \sqrt{R^{3}/GM} \sigma$$. The computational cost of a calculation scales with the total number of points $$M$$ in this grid, while the grid’s resolution — i.e., the spacing between adjacent points — impacts the completeness of the modes found by GYRE (see the Limitations of the Numerical Method section for a discussion of these behaviors in the context of the stretched string BVP).

GYRE constructs a fresh frequency grid for each combination of harmonic degree $$\ell$$ and azimuthal order $$m$$ specified in the &mode namelist groups (see the Namelist Input Files chapter for more details).

The starting

point for each of these grids is the scaffold grid, which comprises the following:

• an inner point $$x=\xin$$;
• an outer point $$x=\xout$$;
• the subset of points of the input model grid satisfying $$\xin < x < \xout$$

By default, $$\xin$$ and $$\xout$$ are obtained from the input model grid as well, meaning that the scaffold grid is identical to the model grid. However, either or both can be overridden using the x_i and x_o parameters, respectively, of the &grid namelist group.

The grid is established