Mapped infinite elements for exterior wave problems

Zienkiewicz, O. C.; Bando, Kiyoshi; Bettess, P.; Emson, C.R.I.; Chiam, T. C.

doi:10.1002/nme.1620210705

Cited by 151 publications

(55 citation statements)

References 10 publications

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“…Whereas in early infinite element concepts 35,36 solely Lagrangian polynomials were used for the radial interpolation functions, Legendre and Jacobi polynomials were found to be a good alternative in terms of improved matrix conditioning and performance. 3,5,6…”

Section: Choice Of Radial Polynomialsmentioning

confidence: 99%

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Moheit

Marburg

2017

J. Comp. Acous.

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Acoustic radiation modes (ARMs) and normal modes (NMs) are calculated at the surface of a fluid-filled domain around a solid structure and inside the domain, respectively. In order to compute the exterior acoustic problem and modes, both the finite element method (FEM) and the infinite element method (IFEM) are applied. More accurate results can be obtained by using finer meshes in the FEM or higher-order radial interpolation polynomials in the IFEM, which causes additional degrees of freedom (DOF). As such, more computational cost is required. For this reason, knowledge about convergence behavior of the modes for different mesh cases is desirable, and is the aim of this paper. It is shown that the acoustic impedance matrix for the calculation of the radiation modes can be also constructed from the system matrices of finite and infinite elements instead of boundary element matrices, as is usually done. Grouping behavior of the eigenvalues of the radiation modes can be observed. Finally, both kinds of modes in exterior acoustics are compared in the example of the cross-section of a recorder in air. When the number of DOF is increased by using higher-order radial interpolation polynomials, different eigenvalue convergences can be observed for interpolation polynomials of even and odd order.

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Section: Choice Of Radial Polynomialsmentioning

confidence: 99%

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Moheit

Marburg

2017

J. Comp. Acous.

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“…The mapped infinite elements were developed by Zienkiewicz et al [18]. These elements are based on polynomial shape functions, attenuating in the infinity.…”

Section: Earlier Infinite Element Methods Workmentioning

confidence: 99%

A formulation of a multi-wave elastodynamic infinite element

Kazakov¹

2007

WIT Transactions on Modelling and Simulation, Vol 46

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In this paper, a formulation of a multi-wave elastodynamic four and eight node infinite element is proposed. Such a kind of element is appropriate for multi-wave soil-structure interaction problems. The formulation follows the standard infinite element formulation steps which are the same as for the Finite element method after mapping the infinite element domain to a finite element domain. It is shown that if only one wave function is used (only one frequency) the proposed multi-wave elastodynamic infinite element is reduced to a singlewave elastodynamic infinite element.The mapping and the Lagrange isoparametric shape functions for a 2D axisymmetric four and eight node multi-wave elastodynamic quadrilateral infinite element are also given. The basic aspects of the continuity along the finite/infinite element (artificial boundary) line are discussed in brief. In this type of model such a line marks the boundary between the near and the far field of the model.The formulation is appropriate for wave propagation problems only.

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“…However, given the oscilliatory nature of the shape functions, more accurate numerical quadrature methods have been developed to perform the integration. The reader is encouraged to read Bettess [4] and Zienkiewicz [18] for detailed information about the integration procedures. This element theoretically has nine nodes.…”

Section: -5 (249)mentioning

confidence: 99%

Acoustic-structure interaction problems. Final report

Love¹,

Taylor²

1993

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Mapped infinite elements for exterior wave problems

Cited by 151 publications

References 10 publications

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

A formulation of a multi-wave elastodynamic infinite element

Acoustic-structure interaction problems. Final report

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