arXiv subjects

Denis Anuprienko

Publications and source records attributed to Denis Anuprienko.

4 recordsLinked to original sources

arXiv2022

Parallel efficiency of monolithic and fixed-strain solution strategies for poroelasticity problems

Poroelasticity is an example of coupled processes which are crucial for many applications including safety assessment of radioactive waste repositories. Numerical solution of poroelasticity problems discretized with finite volume -- virtual element scheme leads to systems of algebraic equations, which may be solved simultaneously or iteratively. In this work, parallel scalability of the monolithic strategy and of the fixed-strain splitting strategy is examined, which depends mostly on linear solver performance. It was expected that splitting strategy would show better scalability due to better performance of a black-box linear solver on systems with simpler structure. However, this is not always the case.

math.NA↗

arXiv2022

First-order continuation method for steady-state variably saturated groundwater flow modeling

Recently, the nonlinearity continuation method has been used to numerically solve boundary value problems for steady-state Richards equation. The method can be considered as a predictor-corrector procedure with the simplest form which has been applied to date having a trivial, zeroth-order predictor. In this article, effect of a more sophisticated predictor technique is examined. Numerical experiments are performed with finite volume and mimetic finite difference discretizations on various problems, including real-life examples.

math.NA↗

arXiv2021

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

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 this 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 on model and real-life problems.

math.NA↗

arXiv2020

Nonlinearity continuation method for steady-state groundwater flow modeling in variably saturated conditions

Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume discretization of steady-state Richards equation, a series of problems with increasing nonlinearity are solved using the Newton method. This approach is compared to pseudo-transient method on several test cases, including real site problems and involving parallel computations.

math.NA↗