Related papers: Algebraic Multigrid Preconditioners for Multiphase…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…
This paper develops a new algebraic multigrid (AMG) method for sparse least-squares systems of the form $A=G^TG$ motivated by challenging applications in scientific computing where classical AMG methods fail. First we review and relate the…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
Challenging aspects of large-scale turbulent edge simulations in plasma physics include robust nonlinear solvers and efficient preconditioners. This paper presents recent advances in the scalable solution of nonlinear partial differential…
In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a…
We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…
Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
The Potts model has many applications. It is equivalent to some min-cut and max-flow models. Primal-dual algorithms have been used to solve these problems. Due to the special structure of the models, convergence proof is still a difficult…
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…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
The construction of multigrid operators for disordered linear lattice operators, in particular the fermion matrix in lattice gauge theories, by means of algebraic multigrid and block LU decomposition is discussed. In this formalism, the…
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous…
Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully…
We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…
This paper investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin (HDG)…
In this paper, we propose a new finite element solution approach to the multi-compartmental Darcy equations describing flow and interactions in a porous medium with multiple fluid compartments. We introduce a new numerical formulation and a…
This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…