{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/preconditioned-nonlinear-conjugate-gradient-2","title":"Preconditioned Nonlinear Conjugate Gradient Method for Real-time Interior-point Hyperelasticity","arxiv_id":"2405.08001","date":"2024-05-06","proceeding":null,"authors":["Xing Shen","Runyuan Cai","Mengxiao Bi","Tangjie Lv"],"abstract":"The linear conjugate gradient method is widely used in physical simulation, particularly for solving large-scale linear systems derived from Newton's method. The nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization, which is extensively utilized in solving practical large-scale unconstrained optimization problems. However, it is rarely discussed in physical simulation due to the requirement of multiple vector-vector dot products. Fortunately, with the advancement of GPU-parallel acceleration techniques, it is no longer a bottleneck. In this paper, we propose a Jacobi preconditioned nonlinear conjugate gradient method for elastic deformation using interior-point methods. Our method is straightforward, GPU-parallelizable, and exhibits fast convergence and robustness against large time steps. The employment of the barrier function in interior-point methods necessitates continuous collision detection per iteration to obtain a penetration-free step size, which is computationally expensive and challenging to parallelize on GPUs. To address this issue, we introduce a line search strategy that deduces an appropriate step size in a single pass, eliminating the need for additional collision detection. Furthermore, we simplify and accelerate the computations of Jacobi preconditioning and Hessian-vector product for hyperelasticity and barrier function. Our method can accurately simulate objects comprising over 100,000 tetrahedra in complex self-collision scenarios at real-time speeds.","url_abs":"https://arxiv.org/abs/2405.08001v1","url_pdf":"https://arxiv.org/pdf/2405.08001v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"preconditioned-nonlinear-conjugate-gradient-2","repo_url":"https://github.com/Xingbaji/PNCG_IPC","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}