The scaled boundary finite element method: Analytical solution in frequency domain
A new procedure derived from the boundary finite element method (BFEM) is presented. This procedure is called the scaled BFEM since the author introduces a scaling parameter \(\xi\). The idea is based on the fact that around a node supporting a shape function \(N(\xi,\eta)\), it is possible to define a new radial coordinate \(\xi\). For a domain with a boundary defined by the segmentation with \(\xi=1\), its interior is defined by a family of shapes with \(\xi< 1\), whereas its exterior is defined by the family of shapes with \(\xi> 1\). By this way, an optimization procedure (such as Galerkin one) provides a system of ordinary differential equations in the radial coordinate \(\xi\). Solving these equations, the authors obtain an analytical solution in frequency domain. Comparison of the proposed procedure with other known methods validate the approach.
system of ordinary differential equations
scientific article; zbMATH DE number 1421618