In this paper, electromagnetic scattering from dielectric objects with negative permittivity is solved by the volume integral equation (VIE)-hierarchical matrix (-matrix)-based fast direct solver. To improve solution efficiency, a coarsening algorithm for the -matrix is used, and the key parameter for the admissible condition is optimized through numerical experiments. Finally, the discontinuous Galerkin (DG) VIE (DGVIE) method is developed for the fast direct solver. It is shown that scattering from inhomogeneous dielectric objects with negative permittivity and with multiscale structure can be analyzed efficiently by the DGVIE--matrix-based fast direct solver.
