Introduction

GS2 calculates response matrices to be used as a part of the implicit time advance algorithm. For large problems the calculation of these matrices can become expensive in both time and memory. Here we discuss various topics of relevance to these matries.

Condition number

When using field_option = 'local' we calculate the condition number of the response matrix. There are several ways to view this condition number:

• Set GK_VERBOSITY >= 1 to write the condition number to screen.
• When running with dump_response = .true. we write the condition number into the netcdf file storing the response matrix. View with ncdump -v condition <response_file> | tail -n 2

When the condition number is large we consider the matrix to be ill-conditioned. In this case we also display the condition number in the <runname>.error file and will write to screen a warning if the module level parameter debug is true.

Saving and restoring the response matrices

As the response matrices can be relatively expensive to calculate it is desirable to be able to reuse these across restarted runs etc. Both field_option = 'local' and field_option = 'implicit' offer the option to dump and read response matrices too/from file. To write the response matrices set field_knobs true and to read existing response matrices set field_knobs.

If read_response is true but the expected files are not found then the code will fallback to calculating the response matrices directly. As such, it is recommended that users set both dump_response = T and read_response = T for non-linear simulations. One file is written per response matrix and we may have up to around nx*ny response matrices per time step. The field_knobs input can be used to indicate a directory in which to write/read response matrices to/from, avoiding cluttering the run directory.

The response matrix files generated can be reused on any processor count and are compatible between field_option = 'implicit' and field_option = 'local' choices.