A panel-free method (PFM) has been developed to solve the radiation and the diffraction problems of floating bodies in the time domain. The velocity potentials due to non-impulsive inputs are obtained by solving the boundary integral equations in terms of source strength distribution. The singularity in the Rankine source of the time-dependent Green function is removed. The geometry of a body surface is mathematically represented by NURBS surfaces. The integral equation can be globally discretized over the body surface by Gaussian quadratures. No assumption is needed for the degree of approximation of distributed source strength on the body surface.

The accuracy of PFM was first demonstrated by its application to a classical problem of uniform flow past a sphere. The radiation and diffraction response functions of a hemisphere at zero speed were then computed by PFM. The PFM was also applied to a Wigley hull. The computed response functions, added-mass and damping coefficients, and the diffraction forces for the hemisphere and the Wigley hull were compared with published results.

Compared with the panel method, the advantages of PFM are:​ (a) less numerical manipulation, since panelization of a body surface is not needed;​ (b) more accurate, since the assumption for the degree of approximation of source strength distribution as in the panel method is not needed and the surface geometry can be described mathematically;​ (c) the integral equation is desingularized before it is discretized so that Gaussian quadrature can be applied directly and globally;​ (d) the Gaussian quadrature points, and their respective Jacobian and normals on the surface can be accurately computed based on the NURBS expression;​ and (e) the accuracy of the solution can be easily controlled by changing the number and/or the arrangement of Gaussian quadrature points.