Related papers: Fast algebraic multigrid for block-structured dens…
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
Problems arising in Earth's mantle convection involve finding the solution to Stokes systems with large viscosity contrasts. These systems contain localized features which, even with adaptive mesh refinement, result in linear systems that…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…
Given a multigrid procedure for linear systems with coefficient matrices $A_n$, we discuss the optimality of a related multigrid procedure with the same smoother and the same projector, when applied to properly related algebraic problems…
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…
We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear-quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the…
We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…
Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…
The Local Fourier analysis (LFA) is a classic tool to prove convergence theorems for multigrid methods (MGMs). In particular, we are interested in optimality that is a convergence speed independent of the size of the involved matrices. For…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening…
This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for…
We present a scheme to solve the nonlinear multigroup radiation diffusion (MGD) equations. The method is incorporated into a massively parallel, multidimensional, Eulerian radiation-hydrodynamic code with adaptive mesh refinement (AMR). The…