Three-Dimensional Desingularized Boundary Integral Methods for Potential Problems

摘要

The concept of desingularization in three-dimensional boundary integralcomputations is reexamined. The boundary integral equation is desingularized by moving the singular points away from the boundary and outside the problem domain. This allows the surface integrals, which become nonsingular, to be evaluated by simpler techniques and speeds the computation. The effects of the distance of desingularization on the solution and the condition of the resulting system of algebraic equations are studied for both the direct and indirect versions of the desingularized boundary integral methods. Computations show that a broad range of desingularization distances gives accurate solutions with significant savings in the computation time. The desingularization distance must be carefully linked to the mesh size to avoid problems with uniqueness and ill-conditioning. As an example, the desingularized indirect approach is used to study unsteady nonlinear three-dimensional gravity waves generated by a moving submerged disturbance; minimal computational difficulties are encountered at the truncated boundary.