Abstract:
A class of mixed boundary value problems (bvps), occurring in the study of scattering of surface
water waves by thin vertical rigid barriers placed in water of finite depth, is examined for their approximate
solutions. Two different placings of vertical barriers are analyzed, namely, (i) a partially immersed barrier and
(ii) a bottom standing barrier. The solutions of the bvps are obtained by utilizing the eigenfunction expansion
method, leading to a mathematical problem of solving over-determined systems of linear algebraic equations.
The methods of analytical least-square approximation as well as algebraic least-square approximation are
employed to solve the corresponding over-determined system of linear algebraic equations and thereby evaluate
the physical quantities, namely, the reflection and transmission coefficients. Further, the absolute values of the
reflection coefficients are compared to the known results obtained by utilizing a Galerkin type of approximate
method after reducing the bvps to integral equations whose complete solutions are difficult to be determined.
Various combinations of discretization of the resulting dual series relations obtained in the present analysis are
employed to determine the least-square solution.
