Steps per wavelength in mesh density

[shpongle]

Hi

Could anyone explain to me the concept and significance of mesh density as a function of steps per wavelength? I am asking this in context of a frequency domain EM-solver.

Thanks

 

[boneh3ad]

It's related to the Nyquist rate for time-varying signals, only in this case it is spatial. If you were to take the Fourier transform of your solution, you would only be able to resolve wavelengths of twice your step size or greater. If you are trying to actually build an accurate time or spatial history of the solution including those wavelengths, you would need to have an even more dense mesh.

 

[shpongle]

It's related to the Nyquist rate for time-varying signals, only in this case it is spatial. If you were to take the Fourier transform of your solution, you would only be able to resolve wavelengths of twice your step size or greater. If you are trying to actually build an accurate time or spatial history of the solution including those wavelengths, you would need to have an even more dense mesh.

Thank you for the reply. Could you clarify a bit more ?

I am simulating a Photonic crystal in a frequency range 185-225 THz. The software which I am using is CST Microwave Studio. I am using tetrahedral meshing for frequency domain solution.

I have to alter mesh density due to computer hardware constraints.

The software provides provides two parameters to do this, namely - "steps per wavelength" and "minimum number of steps". May I ask what does "step" refer to and if there is any way to determine the appropriate number of steps per wavelength and minimum number of steps.

 

[boneh3ad]

Step size usually just means the distance between two points in a given direction. I am not familiar with the software, but it sounds to me like you are setting the spacing and number of data points you are solving. Steps per wavelength is how dense the points are and the minimum number is going to determine how many wavelengths you can capture.

 

[pmacias]

Hello,

Mesh density is an important concept in numerical simulations, particularly in the context of electromagnetic (EM) solvers. It refers to the number of elements or cells used to discretize a given region or volume in a simulation. A finer mesh, with a higher number of elements, is said to have a higher mesh density.

Steps per wavelength, also known as the spatial resolution, is a measure of the number of elements or cells per wavelength of the EM wave being simulated. It is typically used in frequency domain EM-solvers, where the EM fields are described as sinusoidal waves of various frequencies.

The significance of mesh density and steps per wavelength lies in their impact on the accuracy and efficiency of the simulation. A finer mesh with more steps per wavelength can capture more detail and accurately represent the EM fields, but it also requires more computational resources and time. On the other hand, a coarser mesh with fewer steps per wavelength may result in inaccuracies in the simulation results.

In general, it is recommended to use a mesh density that is at least 10 times the number of steps per wavelength, to ensure accurate results. However, the optimal mesh density may vary depending on the specific simulation and its requirements.

I hope this explanation helps clarify the concept of mesh density and its relation to steps per wavelength in the context of frequency domain EM-solvers. Please let me know if you have any further questions.

Best regards,Scientist