Multigrid preconditioners for the hybridised discontinuous Galerkin discretisation of the shallow water equations

DOI10.1016/j.jcp.2020.109948OpenAlexW3097943160MaRDI QIDQ2127012

Eike H. Müller, Jack Betteridge, T. H. Gibson, Ivan G. Graham

Publication date: 19 April 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09389

zbMATH Keywords

multigridpreconditionerselliptic PDEatmospheric modellinghybridised discontinuous Galerkin

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Geophysics (86-XX)

Related Items (1)

Optimal Geometric Multigrid Preconditioners for HDG-P0 Schemes for the reaction-diffusion equation and the Generalized Stokes equations

Uses Software

• PETSc
• MUMPS
• UFL
• chammp
• Firedrake
• Slate

Cites Work

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• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations
• From Godunov to a unified hybridized discontinuous Galerkin framework for partial differential equations
• A review of element-based Galerkin methods for numerical weather prediction: finite elements, spectral elements, and discontinuous Galerkin
• Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
• High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations
• An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• A standard test set for numerical approximations to the shallow water equations in spherical geometry
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Matrix-free multigrid block-preconditioners for higher order discontinuous Galerkin discretisations
• IMEX HDG-DG: a coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for shallow water systems
• High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling
• Direct Methods for Sparse Matrices
• Multigrid for an HDG method
• Construction and Analysis of HDG Methods for Linearized Shallow Water Equations
• A convergent multigrid cycle for the hybridized mixed method
• A hybrid mixed discontinuous Galerkin finite-element method for convection-diffusion problems
• A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
• Firedrake
• Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Finite Volume Methods for Hyperbolic Problems
• Solver Composition Across the PDE/Linear Algebra Barrier
• Implicit-Explicit Methods for Time-Dependent Partial Differential Equations
• Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
• An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number
• Unified form language
• Methods of conjugate gradients for solving linear systems

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