The stability of infinite element schemes for transient wave problems

Astley, R.J.; Hamilton, J. A.

doi:10.1016/j.cma.2005.01.026

Cited by 15 publications

(8 citation statements)

References 18 publications

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“…As has been indicated in [26] the required condition for stability of the infinite elements is the semi-positive definiteness of the mass matrix. This was also shown numerically by Astley and Hamilton [18], where the authors concluded that for mapped elements only stable results are acquired when the infinite elements are locally orthogonal to the interface, which happens when the interface is a sphere. The authors show that in this specific case the mass matrix for the infinite elements is zero, and that if the mass matrix is not exactly zero, due to small inconsistencies in the geometry, that the system becomes unstable, because the mass matrix loses its semi-positive definiteness properties.…”

Section: Stability Considerations For Different Formulationssupporting

confidence: 53%

“…When a spherical IE boundary is added, the contribution of the IEs to the mass matrix is zero [18], thus M a,12 , M a,21 and M a,22 are zero, and the reduced order matrix will have the following definition:…”

Section: Applying Mor On the Whole System Simultaneouslymentioning

confidence: 99%

“…Several numerical techniques are available to implement this boundary condition. The most well known techniques are the Perfectly Matched Layer (PML) [14], the absorbing boundary condition (ABC) [15], the Dirichlet to Neumann map [13] and Infinite Elements (IE) [16,17,18,19]. The PML is widely used for vibro-acoustics, but mainly in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stable model order reduction for time-domain exterior vibro-acoustic finite element simulations

Ophem

Atak

Deckers

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This paper presents a novel method that enables model order reduction of a fully-coupled, exterior vibro-acoustic finite element model for time domain simulations. The method preserves the stability of the full model and reduces the amount of degrees of freedom significantly, with only a moderate amount of calculation complexity. Infinite elements are used on the finite element boundary to satisfy the Sommerfeld radiation condition. Two different strategies to calculate the reduced order model are compared. The first strategy works with a split reduced basis and can be applied on any fully stable model. The second strategy starts from a modified Everstine formulation and directly builds a reduced basis from the full model, leading to more compact reduced order models. Furthermore, a method is derived to perform explicit time integration on the reduced system, while avoiding the inversion of the mass matrix, which might not be possible due to the presence of the infinite elements. Also this method is shown to preserve the stability of the model and a computationally efficient way for implementation of the method is discussed. The effectiveness of the novel methodology is demonstrated with two numerical models.

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Section: Stability Considerations For Different Formulationssupporting

confidence: 53%

Section: Applying Mor On the Whole System Simultaneouslymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stable model order reduction for time-domain exterior vibro-acoustic finite element simulations

Ophem

Atak

Deckers

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…This has important implications in the stability of the time integration, as outlined in. 82 In terms of discretizing the infinite domain, infinite elements can be classified into 2 main approaches: the separable approach, and the mapped approach. In the separable approach, the exterior domain is assumed to be in a separable coordinate system, such as spherical or spheroidal.…”

Section: Infinite Elements For Acousticsmentioning

confidence: 99%

Sierra/SD Theory Manual.

Bunting¹,

Crane²,

Day³

et al. 2018

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Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Sierra/SD. For a more detailed description of how to use Sierra/SD , we refer the reader to Sierra/SD, User's Notes. Many of the constructs in Sierra/SD are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Sierra/SD are specific to our implementation. We try to be far more complete in those areas.

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“…This has important implications in the stability of the time integration, as outlined in. 81 In terms of discretizing the infinite domain, infinite elements can be classified into 2 main approaches: the separable approach, and the mapped approach. In the separable approach, the exterior domain is assumed to be in a separable coordinate system, such as spherical or spheroidal.…”

Section: D7 Infinite Elements For Acousticsmentioning

confidence: 99%

Salinas : theory manual.

Walsh¹,

Reese²,

Bhardwaj³

2011

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Salinas provides a massively parallel implementation of structural dynamics finite element analysis, required for high fidelity, validated models used in modal, vibration, static and shock analysis of structural systems. This manual describes the theory behind many of the constructs in Salinas. For a more detailed description of how to use Salinas , we refer the reader to Salinas, User's Notes.Many of the constructs in Salinas are pulled directly from published material. Where possible, these materials are referenced herein. However, certain functions in Salinas are specific to our implementation. We try to be far more complete in those areas.The theory manual was developed from several sources including general notes, a programmer notes manual, the user's notes and of course the material in the open literature.3 4

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The stability of infinite element schemes for transient wave problems

Cited by 15 publications

References 18 publications

Stable model order reduction for time-domain exterior vibro-acoustic finite element simulations

Stable model order reduction for time-domain exterior vibro-acoustic finite element simulations

Sierra/SD Theory Manual.

Salinas : theory manual.

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