Numerical Solution of a Class of Moving Boundary Problems with a Nonlinear Complementarity Approach

Chapiro, Grigori; Gutierrez, Angel E. R.; Herskovits, José; Mazorche, Sandro R.; Pereira, Weslley

doi:10.1007/s10957-015-0816-7

Cited by 5 publications

(3 citation statements)

References 22 publications

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“…at each iteration, with ρk → 0 for k → ∞. In this way, Equation ( 16) replaces (12) and, together with Equation (11), it generates a sequence {p (k) , r (k) } which strictly satisfies the non-negativity conditions in (14). Equation ( 8) is instead satisfied in the limit.…”

Section: The Damped Inexact Newton Iterationmentioning

confidence: 99%

“…Although the procedure we propose is general, it seems appropriate to present it with special regard to a specific problem, which, in our case, is the aforementioned cavitation in hydrodynamic lubrication. This idea follows [11], where a procedure based on an inexact Newton iteration with Armijo backtracking condition has been used for solving practical problems concerning oxygen diffusion and combustion. In particular, we refer to the model of cavitation in hydrodynamic lubrication presented in [12], where the authors reformulated the problem so that pressure and a variable related to density are complementary in the entire domain ( [13]).…”

Section: Introductionmentioning

confidence: 99%

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An inexact Newton method for solving complementarity problems in hydrodynamic lubrication

Mezzadri

Galligani

2018

Calcolo

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We present an iterative procedure based on a damped inexact Newton iteration for solving Linear Complementarity Problems. We introduce the method in the framework of a popular problem arising in mechanical engineering: the analysis of cavitation in lubricated contacts. In this context, we show how the perturbation and the damping parameter are chosen in our method and we prove the global convergence of the entire procedure. A Fortran implementation of the method is finally analyzed. First, we validate the procedure and analyze all its components, performing also a comparison with a recently proposed technique based on the Fischer-Burmeister-Newton iteration. Then, we solve a 2D problem and provide some insights on an efficient implementation of the method exploiting routines of the Lapack and of the PETSc packages for the solution of inner linear systems.

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Section: The Damped Inexact Newton Iterationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An inexact Newton method for solving complementarity problems in hydrodynamic lubrication

Mezzadri

Galligani

2018

Calcolo

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“…1–3 For instance, the famous Karush–Kuhn–Tucker conditions of nonlinear programming, 4 the advection-diffusion control problems, 5 the American-style option pricing problems, 6,7 and the moving boundary problems. 8 Such problems can be modeled as finite-dimensional nonlinear complementarity problems NCPs of weak nonlinearity by resorting to some discretization schemes (e.g. 5-point difference method, time-state discretization, and grid method).…”

Section: Introductionmentioning

confidence: 99%

Inexact fixed-point iteration method for nonlinear complementarity problems

Song,

Zhang,

Zeng

et al. 2023

Journal of Algorithms & Computational Technology

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Based on the modulus decomposition, the structured nonlinear complementarity problem is reformulated as an implicit fixed-point system of nonlinear equations. Distinguishing from some existing modulus-based matrix splitting methods, we present a flexible modulus-based inexact fixed-point iteration method for the resulting system, in which the subproblem can be solved approximately by a linear system-solver. The global convergence of the proposed method is established by assuming that the system matrix is positive definite. Some numerical comparisons are reported to illustrate the applicability of the proposed method, especially for large-scale problems.

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