The Approximate Solving Methods Of The Helmholtz Equation With Damping Boundary Conditions

In this paper, we discuss the numerical solutions of the Helmholtz equation with damping boundary conditions:Where G (?) R~2 is a bounded domain with sufficiently smooth boundary T. k ∈ C is called wave number and A surface damping.D.Colton and R.Kress [1] proved the existence and uniqueness of the above probelm. The aim of this thesis is to study the numerical solutions of the problem. By employing the potential theorem, we convert problem (*) into an equivalent integral equation which has a unknown density function to be determined. Hence the key of this project becomes to find the numerical solutions for this density function and consequently the numerical solutions to the integral equation are obtained. To this end, we first apply the boundary condition to derive the Symm's integral equation of the second kind and then study the numerical solutions to the Symm's integral equation as well as the convergence of these solutions.