Comparison of nonlinear solvers within continuation method for steady-state variably saturated groundwater flow modelling-Reference-Cited by-同舟云学术

Comparison of nonlinear solvers within continuation method for steady-state variably saturated groundwater flow modelling

Published:2021-08-01 Issue:4 Volume:36 Page:183-195
ISSN:0927-6467
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Anuprienko Denis¹²

Affiliation:

1. Marchuk Institute of Numerical Mathematics , Russian Academy of Sciences , Moscow , 119333 , Russia

2. Nuclear Safety Institute , Russian Academy of Sciences , Moscow , 115191 , Russia

Abstract

Abstract Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search algorithm was used to solve the intermediate problems. In the present paper, other solvers such as Picard and mixed Picard–Newton methods are considered, combined with slightly modified line search approach. Numerical experiments are performed with advanced finite volume discretizations for model and real-life problems.

Publisher

Walter de Gruyter GmbH

Subject

Modelling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2021-0016/pdf

Reference34 articles.

1. I. Aavatsmark, T. Barkve, O. B⊘e, and T. Mannseth, Discretization on unstructured grids for inhomogeneous, anisotropic media, Part I: Derivation of the methods. SIAM J. Sci. Comp. 19 (1998), No. 5,1700-1716.

2. E. L. Allgower and K. Georg, Introduction to Numerical Continuation Methods. SIAM, 2003.

3. D. Anuprienko and I. Kapyrin, Nonlinearity continuation method for steady-state groundwater flow modeling in variably saturated conditions. J. Comp. Appl. Math. (2021), 113502.

4. D. Anuprienko and I. Kapyrin, Modeling groundwater flow in unconfined conditions: numerical model and solvers’ efficiency. Lobachevskii J. Math. 39 (2018), No. 7, 867-873.

5. L. Armijo, Minimization of functions having Lipschitz continuous first partial derivatives. Pacific J. Math. 16 (1966), No. 1, 1-3.

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