Generalised Convolution Quadrature with Runge‐Kutta methods for Acoustic Boundary Elements

Abstract

In time domain boundary element formulations the convolution in time can be handled by analytical integration or the convolution quadrature method. Here, the generalised convolution quadrature method is applied based on Runge-Kutta methods. This method allows a variable time step size and the usage of higher order methods in time. The example shows that the variable time step size preserves the convergence order for non-smooth solutions. The order of convergence is restricted by the low order spatial discretisation.

On hybrid convolution quadrature approaches for modeling time‐domain wave problems with broadband frequency content

“…Substituting the definition of w Δt,𝜆 j (16) into (17), then multiplying by 𝜆 n and applying a discrete Fourier transform with respect to n gives where…”

“…This reduces the dimensionality of the problem and hence the complexity of the calculation. Other examples of work on the CQBEM for solving a range of problems can be found in References 11‐18. Of particular relevance to the present study is the work of Reference 18, which proposes a similar hybrid approach to the one introduced here.…”