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In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…

Computational Engineering, Finance, and Science · Computer Science 2022-08-02 G. Guillamet , M. Rivero , M. Zavala-Aké , M. Vázquez , G. Houzeaux , S. Oller

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

In the subsurface, fractures and the surrounding porous rock can deform in interaction with fluid flow. Advanced mathematical models governing these coupled processes typically combine fluid flow, poroelasticity, and fracture contact…

Numerical Analysis · Mathematics 2026-03-03 Marius Nevland , Inga Berre , Jakub Wiktor Both , Eirik Keilegavlen

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful…

Plasma Physics · Physics 2026-05-21 Mark F. Adams , Jin Chen , Benjamin Sturdevant

Most research on preconditioners for time-dependent PDEs has focused on implicit multi-step or diagonally-implicit multi-stage temporal discretizations. In this paper, we consider monolithic multigrid preconditioners for fully-implicit…

Numerical Analysis · Mathematics 2023-02-28 Razan Abu-Labdeh , Scott MacLachlan , Patrick E. Farrell

Venous valves are bicuspidal valves that ensure that blood in veins only flows back to the heart. To prevent retrograde blood flow, the two intraluminal leaflets meet in the center of the vein and occlude the vessel. In fluid-structure…

Numerical Analysis · Mathematics 2018-05-04 Sara Calandrini , Eugenio Aulisa

Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…

Mathematical Physics · Physics 2024-06-04 François Gay-Balmaz , Cesare Tronci

Fluid-solid interaction (FSI) problems are fundamental in many scientific and engineering applications, yet effectively capturing the highly nonlinear two-way interactions remains a significant challenge. Most existing deep learning methods…

Machine Learning · Computer Science 2026-03-03 Shilong Tao , Zhe Feng , Shaohan Chen , Weichen Zhang , Zhanxing Zhu , Yunhuai Liu

Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…

Numerical Analysis · Mathematics 2021-05-24 Jakub W. Both , Kundan Kumar , Jan M. Nordbotten , Iuliu Sorin Pop , Florin A. Radu

In this work, we consider fracture propagation in nearly incompressible and (fully) incompressible materials using a phase-field formulation. We use a mixed form of the elasticity equation to overcome volume locking effects and develop a…

Numerical Analysis · Mathematics 2022-02-10 Timo Heister , Katrin Mang , Thomas Wick

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…

Numerical Analysis · Mathematics 2019-02-20 Ju Liu , Alison L. Marsden

We propose a model for the coupling between free fluid and a linearized poro-hyperelastic body. In this model, the Brinkman equation is employed for fluid flow in the porous medium, incorporating inertial effects into the fluid dynamics. A…

Numerical Analysis · Mathematics 2024-07-19 Aparna Bansal , Nicolás A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…

Numerical Analysis · Mathematics 2021-01-01 Davide Illiano , Jakub Wiktor Both , Iuliu Sorin Pop , Florin Adrian Radu

In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several preconditioners for the classical three-filed Biot model under the…

Numerical Analysis · Mathematics 2020-07-15 Shuangshuang Chen , Qingguo Hong , Jinchao Xu , Kai Yang

We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified…

Numerical Analysis · Mathematics 2025-07-22 Wietse M. Boon , Xiaozhe Hu , Xue Wang

In this work, we develop a cut-based unfitted finite element formulation for solving nonlinear, nonstationary fluid-structure interaction with contact in Eulerian coordinates. In the Eulerian description fluid flow modeled by the…

Numerical Analysis · Mathematics 2025-03-24 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

Parameter-dependent discretizations of linear fluid-structure interaction problems can be approached with low-rank methods. When discretizing with respect to a set of parameters, the resulting equations can be translated to a matrix…

Numerical Analysis · Mathematics 2020-04-23 Peter Benner , Thomas Richter , Roman Weinhandl

In this paper a new monolithic Eulerian formulation in the framework of non-classical continuum is presented for the analysis of fluid-strucuture interaction problems. In this respect, Cosserat continuum theory taking into account the…

Numerical Analysis · Mathematics 2022-04-08 Nazim Hussain , Muhammad Sabeel Khan , Lisheng Liu

In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction. The a posteriori error estimator is realized using the dual-weighted residual method in which the adjoint…

Numerical Analysis · Mathematics 2021-05-25 Thomas Wick