Water wave diffraction analysis by boundary elements

AbstractThis paper presents a mathematical formulation for the boundary element method and its application in solving water-wave-related boundary value problems. The approach presented here permits relation of the method to other numerical techniques, such as finite elements, and more importantly gives an easy and flexible way of introducing and implementing boundary elements. The introduction of many useful concepts now widely used by the finite-element method would give us a better understanding of the fundamental principles shared by the two methods and of their basic difference, hence the possibility of better selection, combination, and mutual contribution of these two powerful methods for solving particular problems. Two examples of water wave diffraction have been provided. Some of the results are for boundary elements as well as water wave diffraction. Comparison of the computed results with existing numerical and analytical results shows excellent agreement