Desingularized boundary integral equation methods (DBIEM) and their applications in water wave dynamics and body motion dynamics over the past 30 years are reviewed. In solving the potential flow problem for wave dynamics, unlike conventional boundary integral methods, a DBIEM 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 thus a fast numerical solution. The paper reviews the fundamental aspects and advantages of DBIEMs. Examples of applications of DBIEMs in wave dynamics and body motion dynamics are given and the outlook of future DBIEMs development is discussed.

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