Time‐domain analysis of wave propagation in unbounded domains based on the scaled boundary finite element method

Birk, Carolin

doi:10.1002/pamm.200910024

Cited by 3 publications

(3 citation statements)

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“…Only 2D situations have been addressed in Reference , which, in combination with the technique of reduced set of base functions, could be reduced to at most 10 DOFs. Parameter studies show that its application to large‐scale problems is problematic. For systems with many DOFs and high‐orders of expansion, the numerical steps involved in the original continued‐fraction approach may become ill‐conditioned.…”

Section: Improved Continued‐fraction Solution Of Dynamic Stiffnessmatrixmentioning

confidence: 99%

“…This facilitates the solution of the dynamic stiffness as continued fractions, but the transmitting boundary has to be placed at a distance away from the interface. Numerical studies reveal that the extension to large‐scale problems is challenging. The method may fail for systems with a larger number of DOFs and for approximations of higher‐order than those considered in Reference .…”

Section: Introductionmentioning

confidence: 99%

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An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains

Birk

Prempramote

Song

2011

Numerical Meth Engineering

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SUMMARYA high-order local transmitting boundary to model the propagation of acoustic or elastic, scalar or vectorvalued waves in unbounded domains of arbitrary geometry is proposed. It is based on an improved continuedfraction solution of the dynamic stiffness matrix of an unbounded medium. The coefficient matrices of the continued-fraction expansion are determined recursively from the scaled boundary finite element equation in dynamic stiffness. They are normalised using a matrix-valued scaling factor, which is chosen such that the robustness of the numerical procedure is improved. The resulting continued-fraction solution is suitable for systems with many DOFs. It converges over the whole frequency range with increasing order of expansion and leads to numerically more robust formulations in the frequency domain and time domain for arbitrarily high orders of approximation and large-scale systems. Introducing auxiliary variables, the continued-fraction solution is expressed as a system of linear equations in i! in the frequency domain. In the time domain, this corresponds to an equation of motion with symmetric, banded and frequency-independent coefficient matrices. It can be coupled seamlessly with finite elements. Standard procedures in structural dynamics are directly applicable in the frequency and time domains. Analytical and numerical examples demonstrate the superiority of the proposed method to an existing approach and its suitability for time-domain simulations of large-scale systems.

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Section: Improved Continued‐fraction Solution Of Dynamic Stiffnessmatrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains

Birk

Prempramote

Song

2011

Numerical Meth Engineering

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“…Bazyar and Song then developed a high‐order local transmitting boundary based on a continued‐fraction solution of the dynamic stiffness matrix and applied it to two‐dimensional problems. Although the concept presented in Reference is appealing and easy to couple with finite elements, its application to large‐scale problems is not trivial . This is due to numerical problems, such as poor convergence and ill‐conditioning, which have been observed for high‐order approximations and three‐dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method

Chen

Birk

Song

et al. 2013

Numerical Meth Engineering

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A high-order time-domain approach for wave propagation in bounded and unbounded domains is proposed. It is based on the scaled boundary FEM, which excels in modelling unbounded domains and singularities. The dynamic stiffness matrices of bounded and unbounded domains are expressed as continued-fraction expansions, which leads to accurate results with only about three terms per wavelength. An improved continued-fraction approach for bounded domains is proposed, which yields numerically more robust time-domain formulations. The coefficient matrices of the corresponding continued-fraction expansion are determined recursively. The resulting solution is suitable for systems with many DOFs as it converges over the whole frequency range, even for high orders of expansion. A scheme for coupling the proposed improved high-order time-domain formulation for bounded domains with a high-order transmitting boundary suggested previously is also proposed. In the time-domain, the coupled model corresponds to equations of motion with symmetric, banded and frequency-independent coefficient matrices, which can be solved efficiently using standard time-integration schemes. Numerical examples for modal and time-domain analysis are presented to demonstrate the increased robustness, efficiency and accuracy of the proposed method.

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Transient Response Analysis of Underwater Structures Based on Total Field Formulas and Modified High-order Transmission Boundary

Zhao

Yin

2021

Int. J. Comput. Methods

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The scaled boundary finite element method (SBFEM) has obvious advantages in simulating both finite and infinite domains. However, the present high-order transmission boundary of SBFEM has a problem in numerical stability, especially for 3D fluid–structure interaction (FSI) problems. In this paper, a modified method is put forward to improve the numerical stability of the high-order transmission boundary and the total field formulas of the modified high-order transmission boundary are derived. In the transient response analysis, the nonreflecting characteristics of the infinite fluid domain are simulated by the modified high-order transmission boundary, while the impacts loading is calculated by the total field formulas. Several numerical examples are presented to prove the validity of the modified high-order transmission boundary and the total field formulas.

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Time‐domain analysis of wave propagation in unbounded domains based on the scaled boundary finite element method

Cited by 3 publications

References 3 publications

An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains

An improved continued‐fraction‐based high‐order transmitting boundary for time‐domain analyses in unbounded domains

A high‐order approach for modelling transient wave propagation problems using the scaled boundary finite element method

Transient Response Analysis of Underwater Structures Based on Total Field Formulas and Modified High-order Transmission Boundary

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