Handbook of mathematical techniques for wave/structure interactions.

*(English)*Zbl 0989.76001
Boca Raton, FL: Chapman & Hall/ CRC. 304 p. (2001).

The volume is written by two active workers in mathematical methods for the description of wave-structure interactions. Here, a bridge between the purely mathematical approaches and computational methods is built. The list of the included topics can be seen from the contents: (1) The water-wave problem; (2) Eigenfunction expansions; (3) Multipole expansions; (4) Integral equations; (5) The Wiener-Hopf and related techniques; (6) Arrays; (7) Wave interaction with small objects; (8) Variational methods; Appendices: A. Bessel functions; B. Multipoles; C. Principal-value and finite-part integrals; References; Index.

The book is well written, formulae are clearly presented, and graphs are suggestive. As is pointed out in the preface, almost all numerical experiments were performed by the authors themselves. The comments and physical interpretation are very interesting; additionally, at the end of each chapter the reader can find bibliographical notes. One of the main merits of the book is that the reader can grasp the idea of each approximate approach and, at the same time, evaluate the necessary volume of calculations. We strongly recommend the book to those working in the field of fluid, acoustic and electromagnetic wave-structure interactions.

The book is well written, formulae are clearly presented, and graphs are suggestive. As is pointed out in the preface, almost all numerical experiments were performed by the authors themselves. The comments and physical interpretation are very interesting; additionally, at the end of each chapter the reader can find bibliographical notes. One of the main merits of the book is that the reader can grasp the idea of each approximate approach and, at the same time, evaluate the necessary volume of calculations. We strongly recommend the book to those working in the field of fluid, acoustic and electromagnetic wave-structure interactions.

Reviewer: D.Stanomir (Bucureşti)

##### MSC:

76-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to fluid mechanics |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

76Mxx | Basic methods in fluid mechanics |

76Q05 | Hydro- and aero-acoustics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |