The hydrodynamics of a seagoing vessel are numerically modeled through the present invention's new calculative methodology, which uniquely combines vessel boundary characteristics and pseudo-spectral environmental characteristics. Solutions are obtained through mutual transformations between the vessel boundary's irregular grid and the environment's regular pseudo-spectral grid. The pressure at the vessel boundary, an important component of the vessel boundary itself, can be determined via either (i) finite element analysis (which has a Cartesian framework) or (ii) the present invention's new vessel normal vector analysis (which has a non-Cartesian framework); the latter approach avoids the singularity problem that generally besets hydrodynamics-related mathematics. Typical inventive practice implements a computer processing unit and succeeds in finding superior solutions in shorter CPU durations.