Adaptive dual boundary element method for solving oblique incident wave passing a submerged breakwater

Abstract

In this paper, an adaptive mesh scheme in boundary element computations for solving the propagation of oblique incident wave passing a breakwater is developed. The purpose is to demonstrate cost savings engendered through adaptivity. The computation is performed on meshes of constant boundary elements, and are adapted to the solution by locally changing element sizes (h-version). Two error indicators obtained from the dual integral equations are used as local error norm, which are essential ingredients for all adaptive mesh schemes in boundary element method (BEM). The evaluation of two local error norms is the norm between the obtained boundary condition and the given boundary condition. The two error tracking curves are in good agreement with their shapes. Two examples show that the adaptive mesh based on the error indicators converge to the solution more efficiently using the same number of elements than does uniform mesh discretization for each segment of the boundary. To check the validity of the present formulation, the transmission and reflection coefficients are determined by using the developed dual BEM program, and are compared well with those of experiment and analytical solution using the eigenfunction expansion method.