For the discretization of higher order elements, the paper presents a modifying integral domain method to remove the irregular frequencies inherited in the integral equation of wave diffraction and radiation from a surface-piercing body. The set of over determined linear equations obtained from the method is modified into a normal set of linear equations by superposing a set of linear equations with zero solutions. Numerical experiments have also been carried out to find the optimum choice of the size of the auxiliary domain and the discretization on it.
With the improvement of efficiency in the calculation of the Green's function for oscillating sources, integral equation methods are widely used for the calculation of the interaction between waves and structures, as summarized by Garrison (1979), Eatock Taylor and Chau (1992). By the integral equation method, unknowns are only limited on the body surface, so its computer effort is relative less than some other methods, such as the infinite element method. However, for a surface-piercing body, the integral equations of wave diffraction and radiation are unsolvable or not uniquely solvable at the eigen frequencies of the interior Dirichlet problem of the body. This phenomenon is call as the irregular frequency problem. The existence of the irregular frequencies will make the calculation very difficult to carry out. This is especially serious for higher order wave problems, for example, a correct result of the second order problem can only be achieved when the calculations at wave frequency and double wave frequency are both free of irregular frequencies. Theoretically, the eigen frequencies of the interior Dirichlet problem are only some discrete values. But after discretization of boundary elements, the set of linear equations set- up has very large condition numbers in the vicinity of eigen frequencies.