A continued‐fraction‐based high‐order transmitting boundary for wave propagation in unbounded domains of arbitrary geometry

By M. Bazyar, Chongmin Song. International Journal for Numerical Methods in Engineering, 2008

146 citations recorded by the source corpus.

A high‐order local transmitting boundary is developed to model the propagation of elastic waves in unbounded domains. This transmitting boundary is applicable to scalar and vector waves, to unbounded domains of arbitrary geometry and to anisotropic materials. The formulation is based on a continued‐fraction solution of the dynamic‐stiffness matrix of an unbounded domain. The coefficient matrices of the continued fraction are determined recursively from the scaled boundary finite element equation in dynamic stiffness. The solution converges rapidly over the whole frequency range as the order of the continued fraction increases. Using the continued‐fraction solution and introducing auxiliary variables, a high‐order local transmitting boundary is formulated as an equation of motion with symmetric and frequency‐independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable for evaluating the response in the frequency and time domains. Analytical and numerical examples demonstrate the high rate of convergence and efficiency of this high‐order local transmitting boundary. Copyright © 2007 John Wiley & Sons, Ltd.

Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/cc2b65f4f56c60b5c85fb7a749580b1b223e949b

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Citations in the corpus

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method (2015, unknown): “They later developed new techniques to enhance the solution procedures for modeling unbounded domains in frequency and time domains [30, 31].”
A scaled boundary polygon formulation for elasto-plastic analyses (2014, methodology): “This method was developed by Song and Wolf [32] in the late 1990s and has, since its introduction, been applied to many problems in engineering such as wave propagation [33, 34],”
High‐order doubly asymptotic open boundaries for scalar wave equation (2009, methodology): “After the high-frequency continued fraction solution is determined as in Reference [40], the differential equation of the residual term is solved again as a continued fraction, but the constants are determined at the low-frequency limit ( →0).”
The scaled boundary finite element method in structural dynamics (2009, background): “Recently, a continued fraction solution was obtained for the dynamic stiffness matrix of an unbounded domain starting from the scaled boundary finite element method [28].”