Related papers: Large-scale Multigrid with Adaptive Galerkin Coars…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
Uniform convergence of the geometric multigrid V-cycle is proven for HDG methods with a new set of assumptions on the injection operators from coarser to finer meshes. The scheme involves standard smoothers and local solvers which are…
I propose a vertex patch smoother where local problems are solved inexactly by a nested, matrix-free p-multigrid, creating a multigrid-within-multigrid framework. A single iteration of the local solver can be evaluated with…
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…
We deal with the numerical solution of the time-dependent partial differential equations using the adaptive space-time discontinuous Galerkin (DG) method. The discretization leads to a nonlinear algebraic system at each time level, the size…
Matrix-free finite element implementations for large applications provide an attractive alternative to standard sparse matrix data formats due to the significantly reduced memory consumption. Here, we show that they are also competitive…
We propose a state redistribution method for high order discontinuous Galerkin methods on curvilinear embedded boundary grids. State redistribution relaxes the overly restrictive CFL condition that results from arbitrarily small cut cells…
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these…
The bootstrap algebraic multigrid framework allows for the adaptive construction of algebraic multigrid methods in situations where geometric multigrid methods are not known or not available at all. While there has been some work on…
We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null…
Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an…
We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-sup condition for different choices of the polynomial…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
In the frame of isogeometric analysis, we consider a Galerkin boundary element discretization of the hyper-singular integral equation associated with the 2D Laplacian. We propose and analyze an adaptive algorithm which locally refines the…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
In this study, we present an $hp$-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming…
This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…