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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.
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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
56
Concept neighborhoods
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.
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Explore all related topics Closing gaps
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.
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.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
How Fast multipole method connects Entity context
Entity context groups extracted connections by relationship type. Counts show recurrence in the analyzed source; the examples are research signals, not claims about importance.
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, It, KIFMM, KIFMM3d The Kernel-Independent Fast, Laplace, Laplace/Helmholtz, Maxwell, Method Another extracted example is Fast multipole method → Abstract, Chapman, Electromagnetics, Fast Multipole Method Nice, Gibson, Greengard, Hall/CRC, ISBN, JAVA Animation, Leslie Greengard, Moments, Rick Beatson, Rokhlin's, The Method, Walton. Use these groups to spot repeated connection types before inspecting the individual relationships.
Fast multipole method relationships Subject–Predicate–Object triples
Relationships are represented as Subject → Predicate → Object triples. Confidence describes extraction strength, not the real-world importance of a relationship; lower-confidence rows may be contextual rather than explicit.
TTTA extracted 56 structured relationships around Fast multipole method. Examples in this analysis include Fast multipole method → related to External links → Gibson and Fast multipole method → related to External links → Walton. The table shows each extracted connection, where it came from and its confidence.
Subject
Predicate
Object
Confidence
Src
Fast multipole method
related to External links
Gibson
0.60
section
Fast multipole method
related to External links
Walton
0.60
section
Fast multipole method
related to External links
The Method
0.60
section
Fast multipole method
related to External links
Moments
0.60
section
Fast multipole method
related to External links
Electromagnetics
0.60
section
Fast multipole method
related to External links
Chapman
0.60
section
Fast multipole method
related to External links
Hall/CRC
0.60
section
Fast multipole method
related to External links
ISBN
0.60
section
Fast multipole method
related to External links
Abstract
0.60
section
Fast multipole method
related to External links
Greengard
0.60
section
Fast multipole method
related to External links
Rokhlin's
0.60
section
Fast multipole method
related to External links
Rick Beatson
0.60
section
No triples extracted yet.
Related concept clusters Concept neighborhoods
Concept neighborhoods group terms that sit near one another in the extracted graph. They are useful for discovering adjacent language and context, but proximity does not by itself imply a factual relationship.
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
Semantic bridges connect parts of the graph that would otherwise be more separate. A bridge is a structural signal in this analysis, not a claim that the two topic areas are equivalent.
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 ⟂ 16Fast multipole method — Free software· splits 21 ⟂ 6Fast multipole method — Sketch of the algorithm· splits 23 ⟂ 4
Map overview Semantic statistics
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.
Fast multipole method
Nodes27
Edges26
Triples56
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.
