Related papers: Methods toward better Multigrid Solver Convergence

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…

We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a standard multigrid V-cycle, we develop a smoother analogous to…

As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear system arising from a Gauss-Legendre-Lobatto global spectral…

We design and investigate a variety of multigrid solvers for high-order local discontinuous Galerkin methods applied to elliptic interface and multiphase Stokes problems. Using the template of a standard multigrid V-cycle, we consider a…

With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…

Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…

In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…

The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…

We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…

We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR)…

We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…

We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…

It is tested whether machine learning methods can be used for preconditioning to increase the performance of the linear solver -- the backbone of the semi-implicit, grid-point model approach for weather and climate models. Embedding the…

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…

We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…

To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…

The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…

We present a multigrid algorithm for the solution of the linear systems of equations stemming from the $p-$version of the Virtual Element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed…

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…

In this work, a local Fourier analysis is presented to study the convergence of multigrid methods based on additive Schwarz smoothers. This analysis is presented as a general framework which allows us to study these smoothers for any type…