Fast multipole method question. Point charges vs surface charges

In summary, the Fast Multipole Method (FMM) is an algorithm used in computational physics to efficiently calculate the interaction between particles in a large system, particularly point charges or surface charges. It differs from other methods by using a hierarchical approach, reducing the computational complexity and making it faster for large systems. Point charges are particles with a specific position and charge, while surface charges are distributed charges on a surface, both of which can be accurately calculated using the FMM. The choice between point charges and surface charges depends on the system's characteristics, such as number of particles and charge density. However, the FMM may not be as efficient for systems with a small number of particles or highly non-uniform charge distributions.
  • #1
lityk
2
0
In many articles authors describe FMM for particles.
e.g.
http://www.csci.psu.edu/seminars/fallnotes/fmm.pdf
http://www.umiacs.umd.edu/labs/cvl/pirl/vikas/publications/FMM_tutorial.pdf

In other articles authors describe FMM for charged surface.

How does these formulations relates?

Main question: How can I move from FMM formulation for particles to FMM formulation for surfaces?
Is it simply by calculating integral(Mnk) instead of Mnk at first step? And then other steps are the same?
 
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  • #2
The formulation for particles and surfaces are related in that they both rely on the Fast Multipole Method (FMM) to approximate the interactions between the particles or surfaces in the system. The main difference between the two is that in the particle case, the interactions between particles are evaluated using a kernel function, while in the surface case, the interactions between surfaces are evaluated using an integral over the surface. Therefore, to move from an FMM formulation for particles to an FMM formulation for surfaces, one needs to replace the kernel function with the appropriate integral. In addition, the FMM algorithm for surfaces typically requires additional steps to ensure that the computational complexity of the algorithm is kept at a reasonable level.
 

1. What is the Fast Multipole Method (FMM)?

The Fast Multipole Method is an algorithm used in computational physics to efficiently calculate the interaction between particles in a large system. It is especially useful in problems involving point charges or surface charges.

2. How does the FMM differ from other methods used to calculate particle interactions?

The FMM differs from other methods, such as the direct summation method, by using a hierarchical approach to calculate the interactions between particles. This reduces the computational complexity from O(N^2) to O(NlogN), making it much faster for large systems.

3. What are point charges and surface charges?

Point charges are particles with a specific position and charge, while surface charges are distributed charges on a surface. Both types of charges are commonly used in electrostatics problems and can be efficiently calculated using the FMM.

4. When should I use point charges and when should I use surface charges in FMM?

Point charges are ideal for systems with a small number of particles and low charge density, while surface charges are more suitable for systems with a large number of particles and high charge density. However, the choice ultimately depends on the specific problem at hand.

5. Are there any limitations to using the FMM for point charges vs surface charges?

One limitation of using the FMM for point charges is that it is most efficient for systems with a large number of particles. For systems with only a few particles, the direct summation method may be more efficient. Additionally, the FMM may not be accurate for systems with highly non-uniform charge distributions, such as those with sharp edges or corners.

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