A stable boundary element method for modeling transient acoustic radiation

Abstract

Transient acoustic radiation from a closed axisymmetric three-dimensional object is modeled using the time domain boundary element method. The widely reported instability problems are overcome by reformulating the integral equation to obtain a Burton and Miller type equation in the time domain. The stability of such an approach is mathematically justified and supported by subsequent numerical results. The hypersingular integrals which arise are evaluated using a method valid for any surface discretization. Numerical results for the radiation of a spherical wave are presented and compared with an exact solution. The accuracy and stability of the results are verified for several geometrically different radiating objects.

A convolution quadrature Galerkin boundary element method for the exterior Neumann problem of the wave equation

“…In this work we adopt the second approach with a view to the future development of methods for reducing the storage complexity and setup time related to those discussed above. Applying the trapezoidal rule to (54) yields (10); hence, we define A m (s) = s −m A(s) for some m 2 and instead evaluateŵ n ( t, A m ). In order to obtain an approximation of the layer density , we must replace the data f (·, t) ∈ H −1/2 ( ), t ∈ (0, T ), with a function g(·, t) ∈ H −1/2 ( ) where f is given by the mth time derivative of g, f = g (m) , and…”

Towards a full-bandwidth numerical acoustic model

“…The CFIE therefore permits sound emanating from the obstacle model to return to the medium, but discretises sound arriving from the medium, passing that data to the obstacle model and scattering cancelling waves into Ω − . As a side effect of this, it also permits any small amounts of energy entering Ω − due to only approximate cancellation of incident and scattered waves to exit into Ω + without reflection, hence internal cavity resonances do not occur 12 . It would be desirable to create a variant of the CFIE which is valid for a more general class of waves; in this paper we are specifically interested in plane waves travelling in the direction ‫ܓ‬ ܽ,݉ ,݊ .…”

A Transient Boundary Element Method for Acoustic Scattering from Mixed Regular and Thin Rigid Bodies

“…More generally, it has been shown that when 0<α<1 energy flows out of the cavity and it cannot support resonant modes 15 . Consequently, the application of L c has been shown to grant superior stability to L p and L v for a variety of test geometries.…”

“…The dominant mathematical analysis of this phenomenon is the Singularity Expansion Method (SEM) 20,21,22 which expands the continuous time system response into a sum of damped exponentials with poles s n and corresponding spatial modes Φ n : [15] where Φ i (t) represents system excitation. This can be written in discrete time as:…”