Related papers: Nonsymmetric multigrid preconditioning for conjuga…
This work introduces and assesses the efficiency of a monolithic $ph$MG multigrid framework designed for high-order discretizations of stationary Stokes systems using Taylor-Hood and Scott-Vogelius elements. The proposed approach integrates…
The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…
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…
Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…
This work studies a composite minimization problem involving a differentiable function q and a nonsmooth function h, both of which may be nonconvex. This problem is ubiquitous in signal processing and machine learning yet remains…
Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are currently stagnate. This situation has created the well-known bottleneck for…
Since introduction [A. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SISC (2001) DOI:10.1137/S1064827500366124] and efficient parallel implementation [A. Knyazev et…
A hierarchical (triple scale) simulation methodology is presented for the prediction of the dynamical and rheological properties of high molecular weight entangled polymer melts. The methodology consists of atomistic, moderately…
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…
We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural…
A structured preconditioned conjugate gradient (PCG) solver is developed for the Newton steps in second-order methods for a class of constrained network optimal control problems. Of specific interest are problems with discrete-time dynamics…
We have presented a fast method for solving a specific type of block four-by-four saddlepoint problem arising from the finite element discretization of the generalized 3D Stokes problem. We analyze the eigenvalue distribution and the…
In this paper, a vertex-based auxiliary space multigrid(V-ASMG) method as a preconditioner of the PCG method is proposed for solving the large sparse linear equations derived from the linear elasticity equations. The main key of such V-ASMG…
Stochastic Gradient Descent (SGD) has become the method of choice for solving a broad range of machine learning problems. However, some of its learning properties are still not fully understood. We consider least squares learning in…
This work presents stochastic optimization methods targeted at least-squares problems involving Monte Carlo integration. While the most common approach to solving these problems is to apply stochastic gradient descent (SGD) or similar…
Nonlinear Model Predictive Control (NMPC) is a state-of-the-art approach for locomotion and manipulation which leverages trajectory optimization at each control step. While the performance of this approach is computationally bounded,…
The Legendre spectral Galerkin method of self-adjoint second order elliptic equations usually results in a linear system with a dense and ill-conditioned coefficient matrix. In this paper, the linear system is solved by a preconditioned…
Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…