A kernel-independent adaptive fast multipole algorithm in two and three dimensions

By Lexing Ying, George Biros, Denis Zorin. 2004

543 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/6159e97fbc4b582df61ee60710e078b6474309e9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Lexing Ying
2. Vladimir Rokhlin
3. Victor Minden
4. Peter K. Kitanidis
5. William Fong
6. Eric F Darve
7. Michael J. Shelley
8. Leslie Greengard

In Electrical and Electronic Engineering

1. Lexing Ying
2. Victor Minden
3. Peter K. Kitanidis
4. Michael J. Shelley
5. Anima Anandkumar
6. Hongwei Cheng
7. Zydrunas Gimbutas
8. Zong-Yi Li

In Ocean Engineering

1. Michael J. Shelley
2. Victor Minden
3. Lexing Ying
4. Kaushik Bhattacharya
5. Anima Anandkumar
6. Peter K. Kitanidis
7. Kamyar Azizzadenesheli
8. Andrew M. Stuart

Citations in the corpus

• The Dynamics of Microtubule/Motor-Protein Assemblies in Biology and Physics (2016, methodology): “This is done within a GMRES iteration (Saad & Schultz 1986) with specialized preconditioners , with fast matrix-vector multiplications performed using a generalized kernel version of the fast-multipole method for the Stokes equations (Ying et al. 2004).”
• A wideband fast multipole method for the Helmholtz equation in three dimensions (2006, background): “An interesting development of this approach (under certain conditions, leading to remarkably efficient schemes) can be found in [32].”
• The black-box fast multipole method (2009, background): “Extensions to general kernels are possible as evidenced by kernel-independent FMMs, see for example [2,3].”
• Multipole Graph Neural Operator for Parametric Partial Differential Equations (2020, methodology): “Inspired by the fast multipole method (FMM), we propose a novel hierarchical, and multi-scale graph structure which, when deployed with GNNs, captures global properties of the PDE solution operator with a linear time-complexity [22, 48].”
• A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, methodology): “Finally, the infinite lattice sum A1,d is given in terms of the Riemann zeta function for d = 1 and may otherwise be well-approximated using far-field compression techniques related to the fast multipole method (FMM) [22, 54].”
• Efficient methods for large‐scale linear inversion using a geostatistical approach (2012, background): “They broadly fall under the following categories: (1) Tree Codes like Barnes-Hut algorithm [Barnes and Hut, 1986], (2) Fast Multipole Methods [Greengard and Rokhlin, 1987; Ying et al., 2004] and (3) Hierarchical matrices and Adaptive Cross Approximation [Bebendorf, 2000; Börm et al.”
• Fast Direct Methods for Gaussian Processes (2014, methodology): “Taylor series approximations [41] and Monte Carlo methods have been suggested [9], as well as conjugate gradient-type methods combined with trace estimators [15].”