A modified scaled boundary finite-element method for problems with parallel side-faces. Part I. Theoretical developments

A modified scaled boundary finite-element method (SBFEM) for problems with parallel side-faces is presented in this study. To overcome the inherent difficulty of the original SBFEM for domains with parallel side-faces, a new type of local co-ordinate system is proposed. The new local co-ordinate system allows the so-called scaling centre of the SBFEM to move freely along an arbitrary curve and thus eliminates the non-parallel side-face restriction in the original SBFEM. The modified SBFEM equations are derived based on a weighted residual approach. It is found that the modified SBFEM solution retains the analytical feature in the direction parallel to the side-faces and satisfies the boundary conditions at infinity exactly, as in the original SBFEM. This paper develops a complete scaled boundary finite-element solution to a two-dimensional Laplace's equation with Neumann and Robin boundary conditions in a semi-infinite domain with parallel boundaries.