Department of Mathematics


Computational Wave Propagation

Computational modelling of a hydrophone
Computational modelling of a hydrophone, note the standing wave pattern. When using hydrophones, for example, to measure the radiation patterns of baffles, the measurement situation is altered and the standing waves should also be modelled. This is, however, seldom done due to the related computational complexity.

The numerical computation of wave propagation of short wavelengths is a challenging problem. The computation of the wave pattern with standard numerical methods, such as the finite element method, involves the construction and solution of a system of equation with a very large number of unknowns. At 20 kHz which is the upper limit of human hearing and a space the size of a typical office, this number would be of the order of 109.

Recently, other numerical methods for the wave propagation problems have gained a lot of attention. For example, the ultra-weak variation formulation and the discontinuous Galerkin method result in equally accurate but computationally significantly more efficient implementations.

We have largely concentrated on the solution of the practical implementation problems of these methods, such as the model reduction, the computational domain truncation problems and the interface (between solid and fluid) problem. We are about to turn to the related inverse problems now that we think we have the necessary computational arsenal at hand.

 

Researchers at The University of Auckland

 

Other collaborators

  • Doctor Tomi Huttunen
    The University of Eastern Finland, Department of Physics.
  • Professor Peter Monk
    The University of Delaware, Department of Mathematics.