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The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
Analog Ising machines (IMs) occupy an increasingly prominent area of computer architecture research, offering high-quality and low latency/energy solutions to intractable computing tasks. However, IMs have a fixed capacity, with little to…
Electric power distribution systems will encounter fluctuations in supply due to the introduction of renewable sources with high variability in generation capacity. It is therefore necessary to provide algorithms that are capable of…
Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The…
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…
A graph based matching is used to construct aggregation for algebraic multigrid. Effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection diffusion coefficient matrix and problems from Florida…
The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a robust and efficient solution method for a wide range of block-separable convex minimization problems, typically stemming from discretizations of nonlinear and nonsmooth partial…
In this paper, we review the parallel and distributed optimization algorithms based on alternating direction method of multipliers (ADMM) for solving "big data" optimization problem in smart grid communication networks. We first introduce…
An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The modified weak Galerkin bilinear form is simplified without the need of the skeletal…
The high computational complexity and energy consumption of artificial intelligence (AI) algorithms hinder their application in augmented reality (AR) systems. However, mobile edge computing (MEC) makes it possible to solve this problem.…
Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…
Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear…
Parallel-in-time methods have shown success for reducing the simulation time of many time-dependent problems. Here, we consider applying the multigrid-reduction-in-time (MGRIT) algorithm to a voltage-driven eddy current model problem.
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.…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
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 increasing diffusion of distributed energy generation systems requires the development of new control paradigms for the coordination of micro-generators, storage systems, and loads aimed at maintaining the efficiency and the safe…
Efficient energy management is essential for reliable and sustainable microgrid operation amid increasing renewable integration. In this paper, an imitation learning-based framework to approximate mixed-integer Economic Model Predictive…
Decarbonization provides new opportunities to plan energy systems for improved health, resilience, equity, and environmental outcomes, but challenges in siting and social acceptance of transition goals and targets threaten progress.…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…