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Fast multipole method: Overview, Free software & Sketch of the algorithm

The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem. It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they were a single source.

Language: English [EN]
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Fast multipole method topic overview

The analysis highlights Overview, Free software and Sketch of the algorithm as prominent areas in the source structure around Fast multipole method.

Related topics
23
Source areas
3
Connected nodes
26
Extracted relationships
37
Related term clusters
12
Bridge connections
26

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 15 topics
Free software · 5 topics
Sketch of the algorithm · 3 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Sketch of the algorithm

Free software

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Fast multipole method connects Entity context

The extracted context around Fast multipole method shows recurring relationship patterns in the source. For example, Fast multipole method → Asynchronous Multi-Tasking HPX-5, CPU/GPU, DASHMM DASHMM, ExaFMM ExaFMM, FastBEM Free, FastCap, FastFieldSolvers, FastHenry, FMM, FMM3D, Helmholtz, Indiana University, Inria Bordeaux, KIFMM, KIFMM3d The Kernel-Independent Fast, Laplace, Laplace/Helmholtz, Maxwell, Method, Moments Another extracted example is Fast multipole method → Chebyshev, Lagrange, MN, Naively, One, Specifically. Use these groups to spot repeated connection types before inspecting the individual relationships.

Fast multipole method

Top relations

related to Free software · 31
Fast multipole method → Asynchronous Multi-Tasking HPX-5, CPU/GPU, DASHMM DASHMM, ExaFMM ExaFMM, FastBEM Free, FastCap, FastFieldSolvers, FastHenry, FMM, FMM3D, Helmholtz, Indiana University, Inria Bordeaux, KIFMM, KIFMM3d The Kernel-Independent Fast, Laplace, Laplace/Helmholtz, Maxwell, Method, Moments
related to Sketch of the algorithm · 6
Fast multipole method → Chebyshev, Lagrange, MN, Naively, One, Specifically

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

fmm multipole displaystyle method fast one mathcal using expansion tolerance applied complexity also 3d developed problems greengard algorithm sum y-x

Fast multipole method relationships Subject–Predicate–Object triples

TTTA extracted 37 structured relationships around Fast multipole method. Examples in this analysis include Fast multipole method → related to Free software → Puma-EM and Fast multipole method → related to Free software → Method. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Fast multipole methodrelated to Free softwarePuma-EM0.60section
Fast multipole methodrelated to Free softwareMethod0.60section
Fast multipole methodrelated to Free softwareMoments0.60section
Fast multipole methodrelated to Free softwareMultilevel Fast Multipole Method0.60section
Fast multipole methodrelated to Free softwareKIFMM3d The Kernel-Independent Fast0.60section
Fast multipole methodrelated to Free softwareMultipole0.60section
Fast multipole methodrelated to Free softwareFMM0.60section
Fast multipole methodrelated to Free softwarePVFMM An0.60section
Fast multipole methodrelated to Free softwareKIFMM0.60section
Fast multipole methodrelated to Free softwareFastBEM Free0.60section
Fast multipole methodrelated to Free softwareFastFieldSolvers0.60section
Fast multipole methodrelated to Free softwareFastHenry0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Fast multipole method bring nearby vocabulary together. In this analysis, examples include Multipole, Method and N-body. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Fast multipole method
    • Multipole
    • Method
    • N-body
    • Sum
    • Displaystyle
    • -1
    • Applied
    • Y-x
    • 3d
    • Fmm
    • Algorithm
    • Also
  • fast multipole method
    • Multipole
    • Method
    • Also
    • Electromagnetics
    • Moments
    • Expansion
    • Fmm
    • N-body
    • Sum
    • Displaystyle
    • -1
    • Applied
  • multipole expansion
    • Expansion
    • Multipole
    • Introduced
    • Jr
    • Manner
    • Rokhlin
    • Greengard
    • Helmholtz
    • N-body
    • Displaystyle
    • Sum
    • -1
  • method of moments
    • Multipole
    • Also
    • Electromagnetics
    • Moments
    • Mom
    • Solver
    • Fmm
    • Problems
    • Applied
    • Displaystyle
    • N-body
    • Sum
  • hartree–fock method
    • Multipole
    • Also
    • Electromagnetics
    • Moments
    • Fmm
    • Applied
    • Displaystyle
    • N-body
    • Sum
    • -1
    • Y-x
    • Iterative
  • iterative solver
    • Solver
    • Varepsilon
    • Complexity
    • Manner
    • Matrix-vector
    • Mom
    • Log
    • Moments
    • Problems
    • Tolerance
    • Within
    • Mathcal
  • sketch of the algorithm
    • -1
    • Y-x
    • Complexity
    • Matrix
    • Matrix-vector
    • Also
    • Corresponding
    • Sum
    • Displaystyle
    • Fast
    • Method
    • Fmm
  • vladimir rokhlin jr.
    • Introduced
    • Jr
    • Rokhlin
    • Greengard
    • Manner
    • Helmholtz
    • Expansion
    • Fmm
    • One
    • Multipole

Connections between topic areas Semantic bridges

For Fast multipole method, one of the stronger structural bridges in this analysis connects Fast multipole method with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Fast multipole method — Overview · splits 11 ⟂ 16
Fast multipole method — Free software · splits 21 ⟂ 6
Fast multipole method — Sketch of the algorithm · splits 23 ⟂ 4

Map overview Semantic statistics

Fast multipole method

Nodes27
Edges26
Triples37
Avg. degree1.93
Density0.074074
Components1

Source & methodology

TTTA analyzes the structure around Fast multipole method to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Overview, Free software & Sketch of the algorithm, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Fast multipole method · EN edition · Analysis: TopicsToTalkAbout

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