Related papers: HMG -- Homogeneous multigrid for HDG
In this paper, we present a flux-based formulation of the hybridizable discontinuous Galerkin (HDG) method for steady-state diffusion problems and propose a new method derived by letting a stabilization parameter tend to infinity. Assuming…
We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of divergence is imposed on the electric field. Then a Lagrange…
Multigrid solvers for hierarchical hybrid grids (HHG) have been proposed to promote the efficient utilization of high performance computer architectures. These HHG meshes are constructed by uniformly refining a relatively coarse fully…
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…
We present a parallel computing strategy for a hybridizable discontinuous Galerkin (HDG) nested geometric multigrid (GMG) solver. Parallel GMG solvers require a combination of coarse-grain and fine-grain parallelism to improve time to…
We develop and analyze a new hybridizable discontinuous Galerkin (HDG) method for solving third-order Korteweg-de Vries type equations. The approximate solutions are defined by a discrete version of a characterization of the exact solution…
We prove quasi-optimal $L^\infty$ norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) method. Although such estimates are available for conforming…
In [SIAM J. Numer. Anal., 59 (2), 720-745], we proved quasi-optimal $L^\infty$ estimates (up to logarithmic factors) for the solution of Poisson's equation by a hybridizable discontinuous Galerkin (HDG) method. However, the estimates only…
We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…
We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable…
We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations,…
We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and…
Convergence and compactness properties of approximate solutions to elliptic partial differential computed with the hybridized discontinuous Galerkin (HDG) are established. While it is known that solutions computed using the HDG scheme…
We propose a framework that allows us to analyze different variants of HDG methods for the static Maxwell equations using one simple analysis. It reduces all the work to the construction of projections that best fit the structures of the…
This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method. Modern implementations of high-order…
We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG…
We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is…
This study introduces a hybridizable discontinuous Galerkin (HDG) method for simulating low-frequency wave propagation in poroelastic media. We present a novel four-field variational formulation and establish its well-posedness and energy…
Fluid-solid interaction has been a challenging subject due to their strong nonlinearity and multidisciplinary nature. Many of the numerical methods for solving FSI problems have struggled with non-convergence and numerical instability. In…
A method is presented to include irregular domain boundaries in a geometric multigrid solver. Dirichlet boundary conditions can be imposed on an irregular boundary defined by a level set function. Our implementation employs quadtree/octree…