Two projection methods for the solution of Signorini problems

Zhang, Shougui

doi:10.1016/j.amc.2018.01.004

Cited by 6 publications

(3 citation statements)

References 27 publications

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“…Hence, we proved the convergence of Algorithm 3. Moreover, from (35), it follows that the optimal choice for ρ is…”

Section: Proof Of Convergencementioning

confidence: 99%

“…In this paper, we propose a new ADMM [7,21] with an optimal parameter for the unilateral obstacle problem [22][23][24][25][26][27][28][29][30][31], which is based on the extreme eigenvalues of the matrix using the finite difference method (FDM) [6,22,26,32]. The main advantage to this method is the simplicity of selecting the optimal parameter [8,[33][34][35][36][37]. Moreover, the method saves computational time for largescale problems because the iterative matrix is always kept constant.…”

Section: Introductionmentioning

confidence: 99%

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An Optimal ADMM for Unilateral Obstacle Problems

Zhang,

Cui,

Xiong

et al. 2024

Mathematics

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We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem. Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used. The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of the iterative matrix. Several numerical experiments confirm the theoretical findings of this study.

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“…Hence, we proved the convergence of Algorithm 3. Moreover, from (35), it follows that the optimal choice for ρ is…”

Section: Proof Of Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Optimal ADMM for Unilateral Obstacle Problems

Zhang,

Cui,

Xiong

et al. 2024

Mathematics

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“…To this end, the non-linear boundary conditions Equation (4) necessitates a specific design [5,10,13,23]. The projection iterative methods [21][22][23] are such approaches. In the next section we provide an heuristic analysis to outline the connections with the switching method [5].…”

Section: Problem Descriptionmentioning

confidence: 99%

High-order compact scheme finite difference discretization for Signorini's problem

Abide

Mansouri

Cherkaoui

et al. 2020

International Journal of Computer Mathematics

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This paper brings out an analysis of the projection iterative algorithm for the numerical solution of the Signorini problem. The very closed connections with the switching method are highlighted. In addition, the relevance of higher-order discretization for Signorini problem is discussed. Thus, a specific iterative solver is developed to address the present fourth and sixth-order compact scheme discretizations. This method is based on a lower-order preconditioning method. Several numerical experiments have been performed to bring light to the accuracy of such method, despite the lack of smoothness at the Signorini boundary.

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Analysis of the element-free Galerkin method for Signorini problems

Dong

2019

Applied Mathematics and Computation

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Two projection methods for the solution of Signorini problems

Cited by 6 publications

References 27 publications

An Optimal ADMM for Unilateral Obstacle Problems

An Optimal ADMM for Unilateral Obstacle Problems

High-order compact scheme finite difference discretization for Signorini's problem

Analysis of the element-free Galerkin method for Signorini problems

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