Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems
type: Item
instance of: scholarly article
title: Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems
zbMATH Open document ID: 0854.65122
DOI: 10.1007/BF01731987
author: Jussi Rahola
published in: BIT
publication date: 1996-06-09T00:00:00Z
review text: The integral equations of acoustic and electromagnetic scattering generate large dense systems of linear equations. These systems are solved by iterative methods, where the matrix-vector multiplication is computed using a special fast method. The author applies the fast multipole method using potential expansions of the dipole potential in terms of spherical Bessel functions, Legendre polynomials and spherical harmonics. The proposed method is based on the manipulation of truncated potential expansions. Two kinds of errors are introduced in the considered method. Error analysis is given, considering both the truncation error of potential expansions and the errors from the use of numerical integration.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 885557
zbMATH Keywords: error analysis
zbMATH Keywords: integral equations
zbMATH Keywords: acoustic and electromagnetic scattering
zbMATH Keywords: iterative methods
zbMATH Keywords: fast multipole method
zbMATH Keywords: spherical Bessel functions
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: spherical harmonics
zbMATH Keywords: truncated potential expansions
reviewed by: Lechoslaw Hącia
MaRDI profile type: Publication
cites work: Q3331506
cites work: An Implementation of the Fast Multipole Method without Multipoles
cites work: Q5508799
cites work: A Fast Adaptive Multipole Algorithm for Particle Simulations
cites work: Q4060253
cites work: The fast multipole method (FMM) for electromagnetic scattering problems
cites work: Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations
cites work: Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices
cites work: A fast algorithm for particle simulations
cites work: The invariant problem for binary string structures and the parallel complexity theory of queries
cites work: Optimal Numerical Integration on a Sphere
cites work: Preconditioned, Adaptive, Multipole-Accelerated Iterative Methods for Three-Dimensional First-Kind Integral Equations of Potential Theory
cites work: Solution of Dense Systems of Linear Equations in the Discrete-Dipole Approximation
cites work: Rapid solution of integral equations of classical potential theory
cites work: Rapid solution of integral equations of scattering theory in two dimensions
cites work: Diagonal forms of translation operators for the Helmholtz equation in three dimensions
Recommended article: Analysis of a diagonal form of the fast multipole algorithm for scattering theory
Recommended article: On Diagonal Form Fast Multipole Method for an Oscillatory Boundary Integral Equation
Recommended article: Diagonal forms of translation operators for the Helmholtz equation in three dimensions
Recommended article: Sparse diagonal forms for translation operators for the Helmholtz equation in two dimensions
Recommended article: Fast evaluation of three-dimensional transient wave fields using diagonal translation operators
Recommended article: Application of fast multipole method to finite-element boundary-integral solution of scattering problems
Recommended article: Translation operators based on Gaussian beams for the fast multipole method in two dimensions
Recommended article: Multi-level fast multipole solution of the scattering problem.
Recommended article: A fast direct solver for quasi-periodic scattering problems
Recommended article: An improved operator expansion algorithm for direct and inverse scattering computations
description: scientific article; zbMATH DE number 885557