Short note on the mass matrix for Gauss-Lobatto grid points

Abstract

The mass matrix for Gauss-Lobatto grid points is usually approximated by Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix \emph{and} its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in $O(N)$ operations instead of $O(N^2)$.

Cited by in corpus (9)

• SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics
• Solving 3D relativistic hydrodynamical problems with WENO discontinuous Galerkin methods
• High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners
• Efficient Explicit Time Stepping of High Order Discontinuous Galerkin Schemes for Waves
• Simulating magnetized neutron stars with discontinuous Galerkin methods
• Unified discontinuous Galerkin scheme for a large class of elliptic equations
• Conservative and accurate solution transfer between high-order and low-order refined finite element spaces
• Matrix-free GPU-accelerated saddle-point solvers for high-order problems in $H(\mathrm{div})$
• General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method