January 25 - 27, 2007

Sparse convolution quadrature methods for the wave equation

Wendy Kress (MPI Leipzig)

We consider the wave equation in a time domain boundary integral formulation. For the numerical solution , to obtain a stable time discretization, we employ the convolution quadrature method in time, which has been developed by Lubich.

In space, a Galerkin boundary element method is considered. The resulting Galerkin matrices of the original method are fully populated and the computational complexity is proportional to N log2N M2, where M is the number of spatial unknowns and N is the number of time steps.

We present two ways of reducing these costs. The first is an a-priori cutoff strategy, which allows to replace a substantial part of the matrices by 0. The second is a panel clustering approximation, which further reduces the computational cost by approximating subblocks by low rank matrices.

The perturbed problem is analysed and stability results are given.

It is shown that the resulting computational complexity is reduced to N log2N M1+s where s ∼ 1/2 depending on the order of the Galerkin method used in space.

This is joint work with S. Sauter and W. Hackbusch.

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