A modified scaled boundary approach in frequency domain with diagonal coefficient matrices

In order to solve the scaled boundary differential equation in dynamic stiffness, an initial value is needed. This initial value can be obtained using high frequency asymptotic expansion of dynamic stiffness matrix. Expanded dynamic stiffness matrix of unbounded mediums at high frequency was presented by previous researchers based on the fully populated coefficient matrices. In this paper, lumped coefficient matrices are used to modify the scaled boundary procedure. Some extra computational efforts of the original scaled boundary method can be eliminated using the proposed approach. The scaled boundary spectral element method (SBSEM) is used to achieve lumped coefficient matrices. It is shown that the proposed method leads to correct dynamic stiffness matrix. Therefore, it can be applied to solve scaled boundary differential equation of unbounded mediums, efficiently. A comparison between the results of the modified and the original methods is presented and accuracy of the modified method is investigated.