View in EDS

Targeting modulus-based matrix splitting iteration approach for the second-order cone linear complementarity model of three-dimensional frictional contact problems.

Saved in:
Bibliographic Details
Title: Targeting modulus-based matrix splitting iteration approach for the second-order cone linear complementarity model of three-dimensional frictional contact problems.
Authors: Li, Zhizhi1 (AUTHOR) lizhizhi16@mails.ucas.ac.cn, Jin, Yimin2 (AUTHOR) jinyimin14@mails.ucas.ac.cn, Zhang, Huai1 (AUTHOR) hzhang@ucas.ac.cn
Source: Optimization & Engineering. Jun2026, Vol. 27 Issue 2, p1579-1610. 32p.
Subjects: Computational complexity, Linear complementarity problem, Newton-Raphson method, Iterative methods (Mathematics), Matrix decomposition
Abstract: The second-order cone linear complementarity problem (SOCLCP) can be used as a model of contact problems with friction. However, its standard formulation as a SOCLCP cannot be employed to large 3d problems because it requires a matrix inversion, which has a computational complexity of O (N uo 3) . Therefore and here, inspired by the flexibility and structural simplicity of the well known MMS algorithms, we propose the Targeting-MMS algorithm for the SOCLCP model of 3d contact problems with friction. The computational complexity is reduced to O (N uo 2) (or even to O (N uo) ). More importantly, we theoretically provide the optimal parameter for the new algorithm, which is a key point for a iteration method. Numerical results show that the Targeting-MMS algorithm with the proposed optimal parameter can save 85 % - 90 % of the time overhead compared to the MMS algorithms and the semi-smooth Newton method, which are by far the state-of-the-art and commonly used methods for solving the SOCLCP. [ABSTRACT FROM AUTHOR]
Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:The second-order cone linear complementarity problem (SOCLCP) can be used as a model of contact problems with friction. However, its standard formulation as a SOCLCP cannot be employed to large 3d problems because it requires a matrix inversion, which has a computational complexity of O (N uo 3) . Therefore and here, inspired by the flexibility and structural simplicity of the well known MMS algorithms, we propose the Targeting-MMS algorithm for the SOCLCP model of 3d contact problems with friction. The computational complexity is reduced to O (N uo 2) (or even to O (N uo) ). More importantly, we theoretically provide the optimal parameter for the new algorithm, which is a key point for a iteration method. Numerical results show that the Targeting-MMS algorithm with the proposed optimal parameter can save 85 % - 90 % of the time overhead compared to the MMS algorithms and the semi-smooth Newton method, which are by far the state-of-the-art and commonly used methods for solving the SOCLCP. [ABSTRACT FROM AUTHOR]
ISSN:13894420
DOI:10.1007/s11081-025-10066-1