Conditioning of infinite element schemes for wave problems

Abstract

While a number of inÿnite element schemes have been implemented for time-harmonic unbounded wave problems in two and three dimensions, stability and conditioning of these schemes can limit the radial order at which they can be applied. In this paper, the choice of radial basis functions is shown to in uence the condition number of such schemes. This e ect is illustrated for three formulations; the Bettess-Burnett formulation, the conjugated Burnett formulation and the Astley-Leis formulation. Calculated values for the condition number are presented for inÿnite element schemes based on an orthogonal modal decomposition at the ÿnite element=inÿnite element interface, and for more conventional inÿnite element schemes based on a transverse ÿnite element discretization. Ill-conditioning can be avoided in the two conjugated formulations by the selection of a suitable radial basis. In the case of the Bettess-Burnett formulation, the condition number increases rapidly irrespective of the radial basis. The e ect of the condition number on the convergence of the various schemes is also discussed.

A few new (?) facts about infinite elements

“…Conditioning problems have been reported by many authors, see e.g. [2,16]. Similar problems have been encountered in context of using infinite elements for solving exterior Maxwell problems and determining Radar Cross Sections (RCS) [19].…”

A few new (?) facts about infinite elements

“…Conditioning problems have been reported by many authors, see e.g. [2,16]. Similar problems have been encountered in context of using infinite elements for solving exterior Maxwell problems and determining Radar Cross Sections (RCS) [19].…”

Prediction of the aerodynamic noise of an airfoil via the hybrid methods of aeroacoustics

“…A group of 25 microphones (including the considered receiver) are placed around the trailing edge on a semi-circle of 2 m radius (14.75 m considering the chord C = 1 m in the meshes) in order to obtain the directiviy patterns. The SPL in far field is computed using the Infinite Elements 23–29 which provide a direct numerical estimate of the acoustic pressure at all points in the outer domain. ACTRAN uses them to model the unbounded acoustic domain and to avoid the reflection of the acoustic waves into the finite element domain; they act as a non-reflective boundary condition.…”

Investigation of the Variation in Insertion Loss of Vertical Noise Barriers for High-speed Railways at Different Levels of Sound Transmission Loss

“…The finite element-infinite element coupled method is a technique that utilizes the near-field distribution of sound waves to make predictions about the far-field noise [11]. In the two-dimensional finite-element-infinite-element acoustic simulation model for noise barrier sections on high-speed railway bridges shown in figure 2, the region Ω 0 represents the acoustic finite element domain, while Ω 1 denotes the acoustic infinite element domain.…”

A few new (?) facts about infinite elements

“…Conditioning problems have been reported by many authors, see e.g. [2,16]. Similar problems have been encountered in context of using infinite elements for solving exterior Maxwell problems and determining Radar Cross Sections (RCS) [19].…”

Prediction of the aerodynamic noise of an airfoil via the hybrid methods of aeroacoustics

“…A group of 25 microphones (including the considered receiver) are placed around the trailing edge on a semi-circle of 2 m radius (14.75 m considering the chord C = 1 m in the meshes) in order to obtain the directiviy patterns. The SPL in far field is computed using the Infinite Elements 23–29 which provide a direct numerical estimate of the acoustic pressure at all points in the outer domain. ACTRAN uses them to model the unbounded acoustic domain and to avoid the reflection of the acoustic waves into the finite element domain; they act as a non-reflective boundary condition.…”

Investigation of the Variation in Insertion Loss of Vertical Noise Barriers for High-speed Railways at Different Levels of Sound Transmission Loss

“…The finite element-infinite element coupled method is a technique that utilizes the near-field distribution of sound waves to make predictions about the far-field noise [11]. In the two-dimensional finite-element-infinite-element acoustic simulation model for noise barrier sections on high-speed railway bridges shown in figure 2, the region Ω 0 represents the acoustic finite element domain, while Ω 1 denotes the acoustic infinite element domain.…”

A few new (?) facts about infinite elements

“…Conditioning problems have been reported by many authors, see e.g. [2,16]. Similar problems have been encountered in context of using infinite elements for solving exterior Maxwell problems and determining Radar Cross Sections (RCS) [19].…”

Prediction of the aerodynamic noise of an airfoil via the hybrid methods of aeroacoustics

“…A group of 25 microphones (including the considered receiver) are placed around the trailing edge on a semi-circle of 2 m radius (14.75 m considering the chord C = 1 m in the meshes) in order to obtain the directiviy patterns. The SPL in far field is computed using the Infinite Elements 23–29 which provide a direct numerical estimate of the acoustic pressure at all points in the outer domain. ACTRAN uses them to model the unbounded acoustic domain and to avoid the reflection of the acoustic waves into the finite element domain; they act as a non-reflective boundary condition.…”

Investigation of the Variation in Insertion Loss of Vertical Noise Barriers for High-speed Railways at Different Levels of Sound Transmission Loss

“…The finite element-infinite element coupled method is a technique that utilizes the near-field distribution of sound waves to make predictions about the far-field noise [11]. In the two-dimensional finite-element-infinite-element acoustic simulation model for noise barrier sections on high-speed railway bridges shown in figure 2, the region Ω 0 represents the acoustic finite element domain, while Ω 1 denotes the acoustic infinite element domain.…”