Spherical layer charge distribution and multipole expansion

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SUMMARY

The discussion focuses on calculating the electrostatic potential near the origin of a sphere with a random spherical distribution of N charges, where N can be as large as 10^9. The user intends to utilize multipole expansion techniques to significantly reduce computational time, as the traditional method scales with N² while multipole expansion scales with N. Recommendations for resources, including books and papers on this topic, are sought to facilitate understanding and implementation of these calculations.

PREREQUISITES
  • Understanding of electrostatics and potential theory
  • Familiarity with multipole expansion techniques
  • Knowledge of computational methods for large-scale simulations
  • Experience with numerical methods and algorithms
NEXT STEPS
  • Research "Multipole Expansion in Electrostatics" for theoretical foundations
  • Explore "Fast Multipole Method" for efficient computation techniques
  • Study "Electrostatic Potential Calculation Techniques" for practical applications
  • Look into "Numerical Methods for Large N Particle Systems" for advanced algorithms
USEFUL FOR

Physicists, computational scientists, and engineers involved in electrostatics, particularly those working with large charge distributions and seeking efficient computational methods.

Horacius.Rex
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Hi,

I have a random spherical distribution of N charges between radiuses
R1 and R2. N is up to 10^9 or more.I want to calculate the
electrostatic potential closed to the origin of the sphere. R1 and R2
are much bigger than the distance of this point to the origin. So I
thought about using the multipole expansion to calculate the
potential, because it is supposed to reduce the Tcpu a lot, mainly
because in this approach Tcpu proportional to N, and in explicit
electrostatical potential calculation Tcpu proportional to N^2. So,
could you recommendme references in good books or papers or weblinks
with examples of similar calculations ?

Thanks
 
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