On the use of variable order infinite wave envelope elements for acoustic radiation and scattering

Cremers, Luc; Fyfe, K.R.

doi:10.1121/1.411994

Cited by 48 publications

(31 citation statements)

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“…The condition number κ(A) is given by the ratio of the largest to the lowest eigenvalue of the frequency-dependent matrix A and is calculated by power iteration and inverse iteration, respectively. As shown by Babuška et al 41 Cremers et al 42 and Dreyer et al 6 the matrix condition increases with the polynomial order, which leads to ill-conditioned matrices for polynomials of degree > 8 in the case of Lagrange polynomials, whereas Legendre and Jacobi polynomials provide distinctly better-conditioned matrices. Tests performed by the authors of this paper have confirmed this observation, although the choice between the four polynomials had no considerable effect on the modes in exterior acoustics, as will be shown subsequently.…”

Section: Matrix Condition Numbermentioning

confidence: 98%

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: Matrix Condition Numbermentioning

confidence: 98%

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

Moheit

Marburg

2017

J. Comp. Acous.

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“…The main conclusion of this paper is that the special wave ÿnite elements can be combined with classical wave inÿnite elements to achieve solutions to wave problems of high accuracy. It can be conjectured that the special wave ÿnite elements could also be combined with other, more recent wave inÿnite elements which have more general mappings, due to Astley [5], Cremers et al [6,8], Burnett and Holford [9] and others. It would be necessary, of course, to match the directions of wave propagation at the special wave ÿnite element=inÿnite element interface.…”

Section: Resultsmentioning

confidence: 97%

“…The extension of the mapping so as to allow inÿnite elements to have arbitrary pole locations so that they can be placed on arbitrary boundary was applied to wave envelope elements using conjugate weighting functions by Astley [5] and Cremers et al [6], and to the quadratic unconjugated wave inÿnite element by Bettess and Bettess [7]. Cremers and Fyfe [8] developed wave envelope elements using linear or quadratic mapping in the angular direction and a variable order of inÿnite mapping in the radial direction for three dimensional problems. More modern ellipsoidal inÿnite elements have been developed by Burnett and Holford [9] and others.…”

Section: Introductionmentioning

confidence: 99%

Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains

Sugimoto

Bettess

2003

Commun. Numer. Meth. Engng.

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SUMMARYThe theory for coupling of mapped wave inÿnite elements and special wave ÿnite elements for the solution of the Helmholtz equation in unbounded domains is presented. Mapped wave inÿnite elements can be applied to boundaries of arbitrary shape for exterior wave problems without truncation of the domain. Special wave ÿnite elements allow an element to contain many wavelengths rather than having many ÿnite elements per wavelength like conventional ÿnite elements. Both types of elements include trigonometric functions to describe wave behaviour in their shape functions. However the wave directions between nodes on the ÿnite element=inÿnite element interface can be incompatible. This is because the directions are normally globally constant within a special ÿnite element but are usually radial from the 'pole' within a mapped wave inÿnite element. Therefore forcing the waves associated with nodes on the interface to be strictly radial is necessary to eliminate this internode incompatibility. The coupling of these elements was tested for a Hankel source problem and plane wave scattering by a cylinder and good accuracy was achieved. This paper deals with unconjugated inÿnite elements and is restricted to two-dimensional problems.

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“…For high radial orders, though, the early concepts of Astley-Leis elements led to extremely ill-conditioned system matrices [26]. Therefore, it was recommended to avoid both high radial polynomial orders as well as envelopes close to the radiating body [25]. Despite this deÿciency the Astley-Leis elements perform well and are already introduced in professional software packages [33].…”

Section: Stability and Ill-conditioningmentioning

confidence: 99%

Improved conditioning of infinite elements for exterior acoustics

Dreyer

Estorff

2003

Numerical Meth Engineering

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SUMMARYAn optimized version of the so-called mapped wave envelope elements, also known as Astley-Leis elements, is introduced. These elements extend to inÿnity in one dimension and therefore provide an approach to the simulation of exterior acoustical problems in both frequency and time domains. Their formulation is improved signiÿcantly through the proper choice of polynomial bases in the direction of radiation. In particular, certain Jacobi polynomials are identiÿed which behave well with respect to conditioning of the system matrices. As a consequence, the size of the ÿnite element discretization may reduce considerably without any loss of accuracy. In addition, the new polynomial bases lead to superior performance of the inÿnite elements in conjunction with iterative solvers.

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On the use of variable order infinite wave envelope elements for acoustic radiation and scattering

Cited by 48 publications

References 0 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

Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains

Improved conditioning of infinite elements for exterior acoustics

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