Related papers: A Root-Node Based Algebraic Multigrid Method
This paper presents Space-Time MultiGrid (STMG) methods which are suitable for performing topology optimisation of transient heat conduction problems. The proposed methods use a pointwise smoother and uniform Cartesian space-time meshes.…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…
This paper presents centralized and distributed Alternating Direction Method of Multipliers (ADMM) frameworks for solving large-scale nonconvex optimization problems with binary decision variables subject to spanning tree or rooted…
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise…
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…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for computing high dimensional partial differential equations (PDEs) and its software implementation. The C\texttt{++} software package called AdaM-DG,…
The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…
Contemporary macro energy systems modelling is characterized by the need to represent strategic and operational decisions with high temporal and spatial resolution and represent discrete investment and retirement decisions. This drive…
This paper establishes the first theoretical framework for analyzing the rounding-error effects on multigrid methods using mixed-precision iterative-refinement solvers. While motivated by the sparse symmetric positive definite (SPD) matrix…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…
By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known…
We study a class of structured convex optimization problems, which have a two-block separable objective and nonlinear functional constraints as well as affine constraints that couple the two block variables. Such problems naturally arise…
We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints.…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
In this paper, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the…