**Computational Wave Propagation**

## Department of Mathematics

# Computational Wave Propagation

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.

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**