(2)Desingularized boundary integral equations and their applications in wave dynamics and wave–body interaction problems

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Yusong Cao ^a,∗, Robert F. Beck ^b
a C-Z Marine Technology, LLC, Houston, TX, USA
^bDepartment of Naval Architecture and Marine Engineering, The University of Michigan, Ann Arbor, MI, USA
Available online 18 January 2016

Abstract
   Over the past 30 years or so, desingularized boundary integral equations (DBIEs) have been used to study water wave dynamics and body motion dynamics. Within the potential flow modeling, unlike conventional boundary integral methods, a DBIE separates the integration surface and the control (collocation) surface, resulting in a BIE with non-singular kernels. The desingularization allows simpler and faster numerical evaluation of the boundary integrals, and consequently faster numerical solutions. In this paper, derivations of different forms of DBIEs are given and the fundamental aspects and advantages of the DBIEs are reviewed and discussed. Numerical examples of applications of DBIEs in wave dynamics and body motion dynamics are given and the outlook of future development of the desingularized methods is discussed
© 2016 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Desingularized boundary integral equations; Potential flows; Wave dynamics; Wave–body interactions.