# Use FMM or FFT for low-discrepancy sample of atoms?

• 1a2
In summary, the conversation discusses a Master's thesis project that involves using a pseudo-random number generator to change the positions of initial atoms. The advisor suggests using an algorithm to speed up the process instead of computing interactions for each sample. The specific algorithm is not clear, with options such as FMM, FFT, or Multilevel FMM being mentioned. The purpose and distribution of the interactions are also unknown.
1a2
To complete my Master's thesis, I am working on a problem that deals with an arrangement of initial atoms, and their positions are then changed according to a pseudo-random number generator with low discrepancy. My advisor told me that instead of computing the interactions between the atoms for each sample (which would take M*N), I could use an algorithm to make it faster (M+N). He told me to just google it

I'm not sure what algorithm can do this. I'm guessing either the FMM, FFT, or Multilevel FMM would be the algorithm. I thought FFT might work since its used for equispaced points, but we are not dealing with time/frequency here. And I don't see how FMM or Multilevel FMM deal with equispaced points.

Any ideas?

What do you want to calculate? "The interactions" is a very vague description.

How does their distribution look like?

## 1. What is the difference between FMM and FFT?

FMM (Fast Multipole Method) is a numerical algorithm used for calculating long-range interactions between particles in a system. FFT (Fast Fourier Transform) is a mathematical tool used for efficiently computing the discrete Fourier transform. In the context of low-discrepancy sampling of atoms, FMM is used to calculate the forces between particles, while FFT is used to perform the necessary coordinate transformations.

## 2. Why is FMM or FFT used for low-discrepancy sampling of atoms?

FMM and FFT are used for low-discrepancy sampling of atoms because they are both computationally efficient and accurate methods for calculating long-range interactions between particles. This is important for accurately simulating the behavior of atoms in a system.

## 3. How do FMM and FFT contribute to reducing discrepancy in atom sampling?

FMM and FFT contribute to reducing discrepancy in atom sampling by accurately calculating the long-range interactions between particles, which can affect the overall distribution of atoms in a sample. By improving the accuracy of these calculations, FMM and FFT can help reduce discrepancies in the sampled atoms.

## 4. Are there any limitations to using FMM and FFT for low-discrepancy sampling of atoms?

Yes, there are limitations to using FMM and FFT for low-discrepancy sampling of atoms. These methods are most effective for systems with large numbers of particles and can be computationally intensive for smaller systems. Additionally, they may not be suitable for systems with highly non-uniform distributions of particles.

## 5. How does the choice between FMM and FFT affect the results of low-discrepancy sampling of atoms?

The choice between FMM and FFT can have a significant impact on the results of low-discrepancy sampling of atoms. While both methods are accurate, they may differ in terms of computational efficiency and suitability for specific systems. It is important to carefully consider the characteristics of a system before choosing between FMM and FFT for low-discrepancy sampling of atoms.

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