Accuracy goal

accuracy goal is a keyword added in version 2.00.01.02 of the software. It in essence supersedes the older eigenvalue threshold and makes finding modes easier and more reliable.

Usage

accuracy goal should appear before a root finding routine is called, eg before the search modes or dispersion keywords are used

accuracy goal=value

where value is a real value, indicating the target numerical accuracy of n_eff. Minimal acceptable value is 3d-14, a typical value for up to 3 or 4 rings of holes with sixfold symmetry is 1d-13, for more complicated or less symmetric structure values up to 1d-11 can be useful. The root searching algorithm will continue refining a minimum of the determinant until accuracy goal is reached. If this is successful, and an eigenvalue below eigenvalue threshold exists, a mode has successfully been found. If the root searching algorithm fails to refine a minimum to below this accuracy, but acceptable accuracy has been reached the minimum may also be considered to be a mode but a warning message will be issued.

accuracy goal should always be defined in a parameter file (except for scattering calculations).

Relation with eigenvalue threshold

In prior versions of the software eigenvalue threshold had to be adapted through trial and error to each specific problem, taking values between 1 and 1d-27 or less. This is no longer needed - eigenvalue threshold should now be set to 0.1 or so, with accuracy goal taking over as the main criterion determining whether a mode has been found or not.

From the release notes

accuracy goal can be used in two ways:

1. If accuracy goal is set to a small value (say, below 1d-12), the value of eigen_value_threshold basically becomes irrelevant, and can be set to a value as large as 1d-1; the algorithm will then consider that a root is found if its precision is good enough. Since it appears from observations in the last few months that the exact value of the eigenvalue (or determinant) at the root is in fact irrelevant, this way of finding roots should be preferred, although in some pathological cases it could in principle lead to artefact roots (I have yet to see one though). I recommend you set accuracy goal to 1d-13 to 1d-15 depending on the complexity of your problem (a very small value can lead to modes being skipped if the structure is complex), and let eigen_value_threshold be 1d-4 or so. You should also set real_precision_threshold to a value smaller than accuracy goal, but if you don't the software should do it for you.

2. If accuracy goal is set to a larger value, but eigen_value_threshold is small (values as usual), the only thing accuracy goal does is to avoid to compute eigenvalues before a minimum accuracy is reached. This saves time, and is consistent with the way modes were found before this version.

Using the first method, I have observed that Wijngaard tests can improve by orders of magnitude compared to previous versions; furthermore it eliminates the problem of knowing what kind of eigenvalue is acceptable. However too small values of accuracy goal can slow down simulations.