(untitled) (Communications in Computational Physics, 2022)
This study aimed to specialise a directional H^2 (DH^2) compression to matrices arising from the discontinuous Galerkin (DG) discretisation of the hypersingular equation in acoustics. The significant finding is an algorithm that takes a DG stiffness matrix and finds a near-optimal DH^2 approximation for low and high-frequency problems. We introduced the necessary special optimisations to make this algorithm more efficient in the case of a DG stiffness matrix. Moreover, an automatic parameter tuning strategy makes it easy to use and versatile. Numerical comparisons with a classical Boundary Element Method (BEM) show that a DG scheme combined with a DH^2 gives better computational efficiency than a classical BEM in the case of high-order finite elements and hp heterogeneous meshes. The results indicate that DG is suitable for an auto-adaptive context in integral equations.