Publication Abstracts

Greengard et al. 2009

Greengard, L., D. Gueyffier, P.-G. Martinsson, and V. Rokhlin, 2009: Fast direct solvers for integral equations in complex three-dimensional domains. Acta Numerica, 18, 243-275, doi:10.1017/S0962492906410011.

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.

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BibTeX Citation

@article{gr04900a,
  author={Greengard, L. and Gueyffier, D. and Martinsson, P.-G. and Rokhlin, V.},
  title={Fast direct solvers for integral equations in complex three-dimensional domains},
  year={2009},
  journal={Acta Numerica},
  volume={18},
  pages={243--275},
  doi={10.1017/S0962492906410011},
}

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RIS Citation

TY  - JOUR
ID  - gr04900a
AU  - Greengard, L.
AU  - Gueyffier, D.
AU  - Martinsson, P.-G.
AU  - Rokhlin, V.
PY  - 2009
TI  - Fast direct solvers for integral equations in complex three-dimensional domains
JA  - Acta Numerica
VL  - 18
SP  - 243
EP  - 275
DO  - 10.1017/S0962492906410011
ER  -

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