Coursera Flash Sale
40% Off Coursera Plus for 3 Months!
Grab it
Learn about a novel preconditioner called AMG with Filtering (AMGF) designed to address computational challenges in large-scale contact mechanics simulations in this 30-minute conference talk from the MFEM Workshop 2025. Discover how large-scale contact mechanics simulations are crucial in engineering fields like structural design and manufacturing, where frictionless contact problems can be modeled by minimizing energy functionals that are often nonlinear, non-convex, and increasingly difficult to solve with higher mesh resolution. Explore the Newton-based interior-point (IP) filter line-search method as an effective approach for large-scale constrained optimization, understanding how while this method converges rapidly, each iteration requires solving large saddle-point linear systems that become ill-conditioned as the optimization process converges to the optimizer due to IP treatment of contact constraints. Examine how this ill-conditioning can hinder scalability and increase iteration counts as the mesh is refined, and learn about the innovative solution through AMGF, a preconditioner tailored to the Schur complement of the saddle-point system. Understand how this approach builds on the classical algebraic multigrid (AMG) solver routinely used for large-scale elasticity problems by adding specialized subspace correction to filter near null space components arising from enforcement of contact interface constraints. Gain insights from theoretical analysis and numerical experiments on various linear and nonlinear contact problems that demonstrate mesh-independent convergence and robustness to the ill-conditioning that typically plagues IP methods. Recognize how this preconditioner makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios, with general applicability to problems where standard solvers perform well except on low-dimensional subspaces arising from localized constraints, interface conditions, or model heterogeneities.
