Factores determinantes de la violencia hacia la mujer

resolution magnetic field grids. The first thing to notice (in table 4.3) is the significant increase in the computational time between the 1× n_r, n_θ, n_φ and 2× n_r, n_θ, n_φ

resolution grids. The time to calculate the2× n_r, n_θ, n_φ

resolution grid is around a factor of 1000 bigger than the 1× nr, nθ, nφ

resolution grid. This huge increase in computational time is due to the lack of FFT for higher resolutions. There may be some optimisations in the code available for the non-FFT-able grids, but the extra efficiency achievable will not produce anywhere near enough of a time saving to level with the FFT timings. After this there is a simple octupling in time when the grid is doubled which is obvious from the grid sizings. This means that running the PFSS model without the FFT is prohibitively long, especially for cases with high numbers of harmonics. The computation time for theL= 641, 2× nr, nθ, nφ

magnetic field is over 3 weeks compared with just half an hour for the default resolution case using the FFT method. These computational times must then be combined with the analysis time of the MSAT routines which also increase in computation time with an increasing of both grid size and L. This is because of the grid size itself and the number of null points found. Thus these high resolution grids are not really feasible. The other issue is the amount of memory required for the calculations and the file size itself afterwards. The file size for the magnetic field grids at the highest

resolution used here is around60 GBand more memory than that is required during the calculation of the magnetic field. This means high performance machines are required which can again be quite prohibitive.

Given that ideally we need to calculate the PFSS model for large numbers of

harmonics, we really need to use the FFT approach to make any progress quickly. So in the next section we discuss what can be done to aid the situation.

4.5

Attempting To Improve The Model Keeping

The FFT

Back in chapter 3, during the discussion of the PFSS model, we consider the possibilities of the grid resolutions when using an FFT to calculate the PFSS

magnetic field. Although the grid points in theφ direction are fixed by the FFT, the grid resolutions in both the r and θ directions are still free to be picked. So to mitigate the issue of long computational time, we can still increase the grid

spacing to become highly irregular (certainly in the angular directions, where

originally they are approximately uniform), this will allow us to try and increase the grid resolution while keeping computational time to a minimum.

To investigate the effect of this change in the grid resolution on the magnetic

skeleton, we have used several combinations of quadrupling the grid resolution in the

r and θ direction for L= 81 and L= 161 models. These are listed in table 4.6 which provides the same data as in table 4.3 for each of these new different magnetic fields. Firstly, looking at the computational time for each of the new magnetic fields, the only effect the quadrupling of the grid resolution in the r and/orθ direction is a quadrupling of the computational time. This means there are no significant computational penalties with each magnetic field being computed quickly even at high resolutions.

Now we turn our attention to the quantitative magnetic skeleton data in table 4.6. The same analysis has been done on each of the fields as those previously. We see that for both values of L the number of null points found in the fields, in general, increases with increasing grid resolution. However, an increase in n_r has a much smaller effect than increasing n_θ. In fact in the4×n_r case for L= 161, the number of null points has decreased: we suspect that this is due to the removal of false-positives when the higher radial grid resolution is used. It was thought that much of the complexity is at low r and that increasing the grid resolution in the r direction close to the solar surface would increase the number of null points. However this seems to have had the opposite effect. It has instead refined the field close to the base

removing some spurious null points. This would suggest that we actually require both a higher radial and higher angular resolution than the default in the PFSS model. Changing the θ grid has the largest effect and increases the magnetic skeleton in the same qualitative way as increasing all three dimensions. For L= 81, the number of null points increases by 25 % when only nθ is increased and 20 % when both nr and

n_θ are increased (table 4.6). This is about half the increase found when all three dimensions were increased equally. This halving in the increase is also seen for the case when L= 161.

Increasing only n_r increases the number by 5 % forL= 81 and decreases the number of nulls by 3 % for L= 161. These changes are much smaller than the increases due to nθ. So comparing with the L= 81 models given in table 4.3, there is a 50 % total increase in the number of null points possible and half of these can be found by