A Spectral Element Method with Transparent Boundary Condition for Periodic Layered Media Scattering

An accurate triangular spectral element method (TSEM) is developed to simulate acoustic problems in complex computational domains. With Fekete points and Koornwinder-Dubiner polynomials introduced, triangular elements are used in the present method to substitute quadrilateral elements in traditional spectral element method (SEM). The efficiency of discretizing complex geometry is enhanced while high accuracy of SEM is remained. The weak form of the second-order governing equations derived from the linearized Euler equations (LEEs) are solved, and perfectly matched layer (PML) boundary condition is implemented. Three benchmark problems with analytical solutions are employed to testify the exponential convergence rate, convenient implementation of solid wall boundary condition and capable discretization in complex geometries of the present method respectively. An application on Helmholtz resonator (HR) is presented as well to demonstrate the possibility of using the present method in practical engineering. The numerical resonance frequency of HR reaches an excellent agreement with the theoretical result.

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On the formulation and implementation of the stress-free boundary condition over deformed bathymetry using a spectral-element-method-based incompressible Navier–Stokes equations solver

Ocean Modelling ◽

10.1016/j.ocemod.2021.101834 ◽

2021 ◽

pp. 101834

Author(s):

Theodoros Diamantopoulos ◽

Peter J. Diamessis ◽

Marek Stastna

Keyword(s):

Boundary Condition ◽

Free Boundary ◽

Spectral Element Method ◽

Stokes Equations ◽

Spectral Element ◽

Free Boundary Condition ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Stress Free Boundary ◽

Element Method

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Dynamic Analysis of a Composite Structure under Random Excitation Based on the Spectral Element Method

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0050 ◽

2019 ◽

Vol 20 (2) ◽

pp. 179-190

Author(s):

M. R. Machado ◽

L. Khalij ◽

A. T. Fabro

Keyword(s):

Boundary Condition ◽

Dynamic Analysis ◽

Composite Structure ◽

Spectral Element Method ◽

Weight Ratio ◽

Spectral Element ◽

Random Excitation ◽

Structural Dynamic ◽

High Level ◽

Element Method

AbstractThe application of the composite materials in the aeronautical and aerospace industries has been increasing over the last several decades. Compared to conventional metallic materials, they present better strength to weight and stiffness to weight ratio. However, they can also present a high level of uncertainty, mainly associated with the manufacturing processes. Besides the uncertainty in the composite material parameters, which can play a role in the structural dynamic response, randomness can also be associated with boundary condition and external excitation sources. This paper treats the dynamic analysis of a composite beam under random excitation and uncertainties in the boundary condition. The beam is modelled by the spectral element method, a wave propagation technique. Some numerical examples are used to study the influence of random source on the dynamic behaviour of the composite structure.

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