A scalable two-level preconditioner for large-scale contact mechanics
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Large-scale contact mechanics simulations are crucial in engineering. In this work, we employ a Newton-based interior-point approach. We demonstrate that while this method converges rapidly, each iteration requires solving large saddle-point systems that becomes increasingly ill-conditioned near the solution of the contact problem. Such ill-conditioning can hinder scalability and increase iteration counts as the mesh is refined. To address this challenge, we introduce a two-level preconditioner tailored to the Schur complement of the system. Building on a conventional algebraic multigrid solver routinely used for large-scale problems we add a correction that targets contact constraints, significantly improving convergence and robustness. Through theoretical analysis and numerical experiments on various linear and nonlinear contact problems, we showcase that the proposed solver demonstrates mesh-independent convergence. Results indicate that the proposed two-level preconditioner makes contact simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. Extensions to friction are also examined. Petrides, Socratis; Hartland, Tucker; Kolev, Tzanio V.; Lee, Chak Shing; Puso, Michael A.; Solberg, Jerome M.; Chin, Eric B.; Wang, Jingyi; and Petra, Cosmin G. “AMG with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization.” SIAM Journal on Scientific Computing, Vol. 47, No. 1, 2025, pp. A1–A29.
