##  [Fast Multipole Method](/index.php/fast-multipole-method) 

  ##  [Fast Multipole Method](https://mathlogic.quantumdictionary.io/fast-multipole-method-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algorithmic framework that accelerates the evaluation of long-range pairwise interactions (e.g., Coulomb or gravitational potentials) by clustering sources, representing their far-field effect with multipole expansions, translating these expansions between clusters, and evaluating local expansions near targets to reduce the complexity from O(N^2) to near-linear or N log N in practice.