Fast multipole accelerated boundary integral equation methods

By Naoshi Nishimura. 2002

514 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/cc2e6caf0c22a348c041e52bfe60ee8a31ebd91b

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

A Modified Method of Fundamental Solutions with Source on the Boundary for Solving Laplace Equations with Circular and Arbitrary Domains (2007, methodology): “Some efficient methods were provided by employing the adaptive mesh scheme and the FMM to improve the efficiency of the dual BEM (Chen et al. 2002c, 2004b; Kita & Kamiya 1994; Nishimura 2002; Rokhlin 1983; Stewart & Hughes 1997) for solving 2-”
Implicit boundary method for finite element analysis using non‐conforming mesh or grid (2008, methodology): “The computational efficiency has been compared only with traditional FEM and not with other approaches such as boundary integral equation methods with fast multipole acceleration [38] which may be faster for linear problems.”
Simulation of simply cross correlated random fields by series expansion methods (2008, methodology): “FMM is a fast solver of integral equations (see [34] for a review) Application of generalized FMM to KLE approximation has recently been published by Schwab and Todor [45].”
Numerical modeling of extreme rogue waves generated by directional energy focusing (2007, methodology): “A review of the application of this algorithm to BIE methods can be found in [45].”
A wideband fast multipole method for the Helmholtz equation in three dimensions (2006, background): “The history of ‘‘fast’’ techniques of the type used in this paper goes back about 20 years; an excellent review can be found in [25].”
The fast multipole boundary element method for potential problems: A tutorial (2006, unknown): “[21].”
A synthesis of numerical methods for modeling wave energy converter-point absorbers (2012, methodology): “Therefore, the three-dimensional BIEM generally uses accelerated iterative algorithms, such as fast multiple methods [121], and generalized minimal residual methods [122], to reduce the CPU time.”
A new fast multipole boundary element method for solving large‐scale two‐dimensional elastostatic problems (2006, methodology): “When the problem size is large, the estimated cost of the entire process described above is O(N) with N being the number of equations, if the number of terms in the multipole expansions and the number of elements in a leaf are kept constant (see Reference [24] for the estimates).”
A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain (2008, methodology): “2 with fixed values forL = O(N1/2) andQ = O(L2) = O(N), one finds aO(N2) complexity for that approach, as remarked also in [37].”
An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton–Miller formulation (2007, methodology): “For a comprehensive review on the fast multipole method, a state-of-theart review paper was given by Nishimura [41].”