MiS Preprint Repository

This paper deals with the ${\mathcal{H}}^2$-matrix approximation of matrices that arise from a Galerkin boundary element (BEM) discretization in the context of the $\mathbf{E}$-based eddy current model. The BEM operators are dense, thus need to be compressed. They are of complicated structure, i.e., some kernels and basis functions are vector valued, and test and basis functions are not always identical. The ${\mathcal{H}}^2$-matrix approximation technique is applied to the kernels of the four different relevant boundary integral operators. Numerical experiments demonstrate the significant acceleration of an iterative solution procedure by means of matrix compression.