Boundary element method (BEM)

The boundary element method (BEM), also called the panel method, solves potential flow by reducing Laplace’s equation for the velocity potential to a surface integral over the body and, for ship problems, the free surface. Only the boundary is discretized into panels carrying source, doublet, or Rankine singularities, so a 3D problem becomes a 2D mesh and a dense linear system for the unknown strengths. It assumes inviscid, irrotational, incompressible flow, so it captures wave-making and added mass but not viscous drag or separation. It underpins seakeeping radiation-diffraction codes and wave-resistance solvers.