The birth of the boundary element method from conception to application.

*(English)*Zbl 1403.65002Summary: The Boundary Element Method (BEM) has now become a well established numerical technique with a number of computer programmes to its credit oriented towards industrial applications. They are reliable and robust tools which stress its unique features versus finite elements, ie reduced dimensionality which makes it easier to interface it to CAD codes; better accuracy, the elegant way in which moving boundaries are dealt with and the possibility of taking into consideration infinite domains without the need of introducing artificial boundaries. An excellent paper on the early work that led to the development of boundary elements has been given by A. H. D. Cheng and D. T. Cheng [Eng. Anal. Bound. Elem. 29, No. 3, 268–302 (2005; Zbl 1182.65005)] and from which many of the illustrations depicting famous scientists were taken. The present contribution aims to explain further how the methodology developed and consolidated towards the end of the 1970s, beginning of the 1980s.

##### MSC:

65-03 | History of numerical analysis |

01A60 | History of mathematics in the 20th century |

65N38 | Boundary element methods for boundary value problems involving PDEs |

##### Keywords:

boundary elements; virtual work; industrial applications; integral equations; reciprocity principles; Green’s identities
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\textit{C. A. Brebbia}, Eng. Anal. Bound. Elem. 77, iii-x (2017; Zbl 1403.65002)

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##### References:

[1] | Cheng, A.; Cheng, D., Heritage and early history of the boundary element method, Int J Eng Anal Bound Elem, 29, 268-300, (2005) · Zbl 1182.65005 |

[2] | Brebbia, C. A., The boundary element method for engineers, (1978), Pentech Press, London and Halstead Press New York · Zbl 0414.65060 |

[3] | Brebbia, C. A.; Telles, J.; Wrobel, L., Boundary element techniques. theory and applications., (1984), Springer Verlag Berlin and New York · Zbl 0556.73086 |

[4] | Brebbia, C. A.; Dominguez, J., Boundary elements - an introductory course., (1989), WIT Press Southampton & Boston · Zbl 0691.73033 |

[5] | Brebbia, C. A.; Nardini, D., Dynamic analysis in solid mechanics by an alternative boundary element approach, Int J Soil Dyn Earthq Eng, 2, 4, (1983) · Zbl 0548.73061 |

[6] | Partridge, P.; Brebbia, C. A.; Wrobel, L. C., The dual reciprocity boundary element method, (1992), Computational Mechanics Publications · Zbl 0758.65071 |

[7] | PORTELA, A., Dual boundary element analysis of crack growth, (1993), Computational Mechanics Publications Southampton and Boston · Zbl 0788.73004 |

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