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 significantfinding is an algor...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 significantfinding is an algorithm that takes a DG stiffness matrix andfinds 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.展开更多
文摘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 significantfinding is an algorithm that takes a DG stiffness matrix andfinds 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.
