Application of hierarchical matrices to the simulation of wave propagation in fluids.

This paper deals with a coupled finite element/scaled boundary finite element method (FE/SBFEM) and its application to wave propagation problems in fluids in the time domain. This method is already well established and has proven to be an efficient technique for treating radiation problems. In its application to time domain problems, convolution integrals arise. For each time step ti, i matrix–vector multiplications have to be performed, where the involved influence matrix—due to the non-locality in space—is fully populated. This numerical evaluation becomes a significant, time-consuming task for long time calculations, thus decreasing the attractiveness of the method. In this paper, the application of hierarchical matrices (ℋ-matrices) is to overcome this drawback. ℋ-Matrices represent an octree-based clustered low-rank approximation of the original, fully populated matrix and allow a considerable increase in efficiency for matrix–vector products encountered, e.g. in convolution integrals. The application of ℋ-matrices to this method results in an increase in efficiency without noticeable loss in accuracy. Since convolution integrals arise in various large-scale engineering computations the application of ℋ-matrix techniques might turn out to be a highly promising way to pursue. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]