spatial down sampling will effect the output of fdtd,or it just decrease the memory requirement alon

# spatial down sampling

**bkhanaliloo**#2

Dear @muhamed.shafeeq

Spatial downsmapling is the property of the monitor, and affects the spatial resolution of visualized data. So, it wonâ€™t affect FDTD simulation itself, but since it saves less data, it requires less memory.

`Tip: In many cases, using the spatial downsampling option (Geometry tab of the monitor) will give a significant speed up with very little loss of accuracy, as long as the nyquist limit is observed (at least two spatial points per the shortest wavelength). If the mesh size is 15 nm and the wavelength is 400nm, then it might be possible to set the downsampling as large as 10 or 13 (400/15/2 = 13.333).`

https://kb.lumerical.com/en/oleds_simple_2d_oled.html

I hope I could answer your question.

**quentinl**#4

@bkhanaliloo I am wondering what is the relationship between Yee cell size, wavelength, sampling rate, min sampling per cycle, Niquist limit, down sampling time, actual samplingâ€¦These parameters are quite important in setting the Time Field monitor and Frequency Domain Monitor. But I find that the explanation in KB is quite simple and short.

**quentinl**#5

There is a description about Nyquist-Shannon sampling theorem in wiki.https://en.wikipedia.org/wiki/Nyquistâ€“Shannon_sampling_theorem

It seems it a theory about signal process and data acquisition. In Lumerical FDTD Solutions, the electrical field and magnetic field data gotten from the monitor is not exactly the data that from the calculation in the Yee cells. Practically, the electrical field vector and the magnetic field vector are not in the same position in the same Yee cell, thus, the interpolation method is used to obtain the data at the same position or at the nearest position to each. Since interpolation method is used, there might be some issues concerning whether the data points gotten from interpolation can represent the data that from the FDTD calculation. Therefore, some Nyquist limit is used to make sure how to get accurate interpolation. My question is what is the relationship between the parameters in the above snapshot in mathematics and how can people set the proper values of the parameters to obtain exact result. Thanks.

**bkhanaliloo**#6

Hi @quentinl

There are tow types of down sampling:

- Spatial down sampling that controlled from geometry tab:

For every mesh point there will be a value for electromagnetic fields. If you have 10 mesh points, the E field will have 10 points (plus the data in the boundaries). If you use a downsample of 2, then you will have 10/ 5 points and etc. This is spatial downsampling and is discussed above. You need to make sure that there are at least two spatial points per wavelength as is explained above.

- Temporal down sampling controlled from advanced tab:

This quantity depends on the frequency and not the mesh cell. For every mesh point, the field is recorded in time and you need to have at least two point per pulse period (T=1/f). You need to make sure that there are at least two points per frequency to meet Nyquist theorem.

For the definition of the parameters, please visit the link below:

https://kb.lumerical.com/ref_sim_obj_monitors_global_properties.html

I hope this solves the confusion.