Application of boundary integral equation method for modelling unsteady nonlinear water waves

Parallel Efficiency of a Boundary Integral Equation Method for Nonlinear Water Waves

We describe the application of domain decomposition on a boundary integral method for the study of nonlinear surface waves on water in a test case for which the domain decomposition approach is an important tool to reduce the computational effort. An important aspect is the determination of the optimum number of domains for a given parallel architecture. Previous work on heterogeneous clusters ...

A convergent boundary integral method for three-dimensional water waves

We design a boundary integral method for time-dependent, threedimensional, doubly periodic water waves and prove that it converges with O(h3) accuracy, without restriction on amplitude. The moving surface is represented by grid points which are transported according to a computed velocity. An integral equation arising from potential theory is solved for the normal velocity. A new method is deve...

On the collocation method for a nonlinear boundary integral equation

In this paper we study a potential problem with a nonlinear boundary condition. Using the Green representation formula for a harmonic function we reformulate the nonlinear boundary value problem as a nonlinear boundary integral equation. We shall give a brief discussion of the solvability of the integral equation. The aim of this paper, however, is to analyse the collocation method for finding ...

The Boundary Integral Equation Method

Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation

Article history: Received 14 January 2010 Received in revised form 4 April 2010 Accepted 15 April 2010 Available online 21 April 2010