The Application of the Dual Surface Method to Treat the Nonuniqueness in Solving Acoustic Exterior Problems

Mohsen, A.; Piscoya, Rafael; Ochmann, Martin

doi:10.3813/aaa.918449

Cited by 11 publications

(7 citation statements)

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“…We now present the application of the DSIE method to an acoustic radiation problem. Other examples can be found in Mohsen et al (2011). The uniqueness of the solutions at all frequencies is ensured for a non-zero imaginary part of α and a maximum value of δ < λ/2.…”

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 95%

“…The method of Dual Surface Integral Equations (DSIE) is an alternative method applied mostly in electromagnetics, but it can be also used to treat to acoustic problems as shown in Mohsen et al (2011). The DSIE preserves the simplicity of CHIEF and specifies the location of the interior points to ensure uniqueness.…”

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 99%

“…The resulting system of equations does not contain the hypersingularities of Burton and Miller while preserving its square matrix form. A proof of uniqueness is given in Mohsen et al (2011) which also states that δ should be less than λ/2. We now present the application of the DSIE method to an acoustic radiation problem.…”

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 99%

“…However, optimal values are not known a priori for general configurations. In Mohsen et al (2011), a parametric study of the values of α and δ was performed. The results showed that good accuracy was obtained in several cases using α = j and δ = λ/8.…”

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 99%

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Acoustical Boundary Elements: Theory and Virtual Experiments

Piscoya

Ochmann

2015

Archives of Acoustics

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This paper presents an overview of basic concepts, features and difficulties of the boundary element method (BEM) and examples of its application to exterior and interior problems. The basic concepts of the BEM are explained firstly, and different methods for treating the non-uniqueness problem are described. The application of the BEM to half-space problems is feasible by considering a Green's Function that satisfies the boundary condition on the infinite plane. As a special interior problem, the sound field in an ultrasonic homogenizer is computed. A combination of the BEM and the finite element method (FEM) for treating the problem of acoustic-structure interaction is also described. Finally, variants of the BEM are presented, which can be applied to problems arising in flow acoustics.

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Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 95%

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 99%

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 99%

Section: Non-uniqueness At Certain Frequenciesmentioning

confidence: 99%

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Acoustical Boundary Elements: Theory and Virtual Experiments

Piscoya

Ochmann

2015

Archives of Acoustics

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“…The Dual Surface method (DS) was first used in the field of electromagnetic problems and adapted to exterior acoustics as shown in detail in [8]. The basic idea is to generate a virtual second surface inside the structure (Fig.…”

Section: Dual Surface Methodsmentioning

confidence: 99%

Results of an implementation of the dual surface method to treat the non-uniqueness in solving acoustic exterior problems using the boundary element method

Burgschweiger

Schäfer²,

Mohsen

et al. 2013

The Journal of the Acoustical Society of America

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The problem of non-uniqueness (NU) of the solution of exterior acoustic problems when using the boundary element method (BEM) is well known. Methods like the Burton-Miller technique or the CHIEF method are used to solve this challenge at the expense of more complex procedures for handling hypersingular integrals and/or higher computing times due to higher complexity of the algorithm or additional equations. The dual surface method, commonly used for electromagnetic problems, was adapted for acoustic radiation and scattering problems. The basic principles of methods to solve the NU problem are outlined and results for different models and solution procedures are presented, taking into account quality, solution time and the numerical advantages when using iterative solvers.

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