A pedestrian introduction to fast multipole methods

DOI10.1007/s11425-012-4392-0zbMath1259.65187OpenAlexW2254041036MaRDI QIDQ1934469

Lexing Ying

Publication date: 28 January 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4392-0

zbMATH Keywords

numerical examplesHelmholtz equationfast multipole methodmultiscale methodsoscillatory kernelsnon-oscillatory kernels

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (1)

Efficient implementation of the Barnes-Hut octree algorithm for Monte Carlo simulations of charged systems

Cites Work

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• A kernel-independent adaptive fast multipole algorithm in two and three dimensions
• Rapid solution of integral equations of scattering theory in two dimensions
• Diagonal forms of translation operators for the Helmholtz equation in three dimensions
• An algorithm for the rapid evaluation of special function transforms
• A fast directional algorithm for high frequency acoustic scattering in two dimensions
• Construction and complexity of hierarchical matrices
• Fast Directional Multilevel Algorithms for Oscillatory Kernels
• Sparse Fourier Transform via Butterfly Algorithm
• A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
• An Implementation of the Fast Multipole Method without Multipoles
• A fast algorithm for particle simulations

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