Recent advances in scaled boundary methods

The scaled boundary finite element method is a relatively new semi-analytical approach developed by Wolf and Song. This paper shows that the scaled boundary finite element method can be considered to be a subset of a larger class of methods, which can be generically termed 'scaled boundary methods'. The paper examines the scaled boundary finite element method, scaled boundary spectral element methods, and meshless scaled boundary methods. It is demonstrated that both Galerkin and Petrov-Galerkin approaches can be used successfully.