### Abstract

Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.

Original language | English (US) |
---|---|

Pages (from-to) | 243-275 |

Number of pages | 33 |

Journal | Acta Numerica |

Volume | 18 |

DOIs | |

State | Published - May 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Numerical Analysis

### Cite this

*Acta Numerica*,

*18*, 243-275. https://doi.org/10.1017/S0962492906410011

**Fast direct solvers for integral equations in complex three-dimensional domains.** / Greengard, Leslie; Gueyffier, Denis; Martinsson, Per Gunnar; Rokhlin, Vladimir.

Research output: Contribution to journal › Article

*Acta Numerica*, vol. 18, pp. 243-275. https://doi.org/10.1017/S0962492906410011

}

TY - JOUR

T1 - Fast direct solvers for integral equations in complex three-dimensional domains

AU - Greengard, Leslie

AU - Gueyffier, Denis

AU - Martinsson, Per Gunnar

AU - Rokhlin, Vladimir

PY - 2009/5

Y1 - 2009/5

N2 - Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.

AB - Methods for the solution of boundary integral equations have changed significantly during the last two decades. This is due, in part, to improvements in computer hardware, but more importantly, to the development of fast algorithms which scale linearly or nearly linearly with the number of degrees of freedom required. These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions. After reviewing the mathematical foundations of such schemes, we illustrate their performance with some numerical examples, and discuss the potential impact of the overall approach in a variety of settings.

UR - http://www.scopus.com/inward/record.url?scp=77949624887&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949624887&partnerID=8YFLogxK

U2 - 10.1017/S0962492906410011

DO - 10.1017/S0962492906410011

M3 - Article

VL - 18

SP - 243

EP - 275

JO - Acta Numerica

JF - Acta Numerica

SN - 0962-4929

ER -