Related papers: On the use of Multigrid Preconditioners for Topolo…
A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
We present a novel augmented Lagrangian (AL) preconditioner for the solution of linear systems arising from finite element discretizations of elliptic interface problems with jump coefficients. The method is based on the Fictitious Domain…
Bundle adjustment is an important global optimization step in many structure from motion pipelines. Performance is dependent on the speed of the linear solver used to compute steps towards the optimum. For large problems, the current state…
Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…
This work presents a multilevel approach to large--scale topology optimization accounting for linearized buckling criteria. The method relies on the use of preconditioned iterative solvers for all the systems involved in the linear buckling…
We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e., optimal convergence rates with respect to the overall…
This paper considers the design of structures made of engineered materials, accounting for uncertainty in material properties. We present a topology optimization approach that optimizes the structural shape and topology at the macroscale…
This paper presents a machine learning-based framework for topology optimization of self-supporting structures, specifically tailored for additive manufacturing (AM). By employing a graph neural network (GNN) that acts as a neural field…
We present a hierarchical optimization architecture for large-scale power networks that overcomes limitations of fully centralized and fully decentralized architectures. The architecture leverages principles of multigrid computing schemes,…
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…
We develop a parallel-in-time multigrid preconditioner for augmented systems. These saddle-point systems are foundational to numerical optimization. Our preconditioner, when paired with a suitable optimization method, accelerates the…
A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…
Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…
This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…