English
Related papers

Related papers: A note on robust preconditioners for monolithic fl…

200 papers

We consider iterative methods for solving the linearised Navier-Stokes equations arising from two-phase flow problems and the efficient preconditioning of such systems when using mixed finite element methods. Our target application is…

Numerical Analysis · Mathematics 2020-05-18 Niall Bootland , Alistair Bentley , Christopher Kees , Andrew Wathen

We present a study of the effectiveness of asynchronous incomplete LU factorization preconditioners for the time-implicit solution of compressible flow problems while exploiting thread-parallelism within a compute node. A block variant of…

Numerical Analysis · Mathematics 2020-10-06 Aditya Kashi , Siva Nadarajah

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…

Numerical Analysis · Mathematics 2013-02-18 Xiaozhe Hu , Shuhong Wu , Xiao-Hui Wu , Jinchao Xu , Chen-Song Zhang , Shiquan Zhang , Ludmil Zikatanov

This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear…

Numerical Analysis · Mathematics 2022-11-09 Martina Bukac , Anyastassia Seboldt , Catalin Trenchea

This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized…

Computational Engineering, Finance, and Science · Computer Science 2024-08-09 Max Firmbach , Ivo Steinbrecher , Alexander Popp , Matthias Mayr

Preconditioning for overdetermined least-squares problems has received comparatively little attention, and designing methods that are both effective and memory-efficient remains challenging. We propose a class of ILU-based preconditioners…

Numerical Analysis · Mathematics 2026-03-31 Jennifer Scott , Miroslav Tůma

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner-outer GMRES…

Numerical Analysis · Mathematics 2024-04-30 Mehdi Jadoui , Christophe Blondeau , Emeric Martin , Florent Renac , François-Xavier Roux

We present a monolithic approach to large-deformation fluid-structure interaction (FSI) problems that allows for choosing fully implicit, single-step and single-stage time integration schemes in the structure and fluid field independently,…

Numerical Analysis · Mathematics 2023-08-25 Matthias Mayr , Thomas Klöppel , Wolfgang A. Wall , Michael W. Gee

In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block…

Numerical Analysis · Mathematics 2016-06-22 Yicong Ma , Kaibo Hu , Xiaozhe Hu , Jinchao Xu

High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…

Numerical Analysis · Mathematics 2024-06-28 Jakob Vandergrift , Matthew J. Zahr

Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…

Numerical Analysis · Mathematics 2017-01-09 Silvia Gazzola , Yves Wiaux

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

This work develops and analyzes a variational-monolithic unfitted finite element formulation of a linear fluid-structure interaction problem in Eulerian coordinates with a fixed interface. The overall discretization is based on a backward…

Numerical Analysis · Mathematics 2026-03-27 Stefan Frei , Tobias Knoke , Marc C. Steinbach , Anne-Kathrin Wenske , Thomas Wick

This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…

Numerical Analysis · Mathematics 2025-10-21 Volker Mehrmann , Manuel Schaller , Martin Stoll

The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…

Numerical Analysis · Mathematics 2014-02-27 Bryan Quaife , George Biros

We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…

Numerical Analysis · Mathematics 2026-02-10 Lander Besabe , Hyesuk Lee

We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a…

Numerical Analysis · Mathematics 2025-08-19 Maria Vasilyeva , Ben S. Southworth , Shubin Fu

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible…

Numerical Analysis · Mathematics 2020-07-28 Matteo Frigo , Nicola Castelletto , Massimiliano Ferronato , Joshua A. White

We analyse three time integration schemes for unfitted methods in fluid structure interaction. In Alghorithm 1 we propose a fully discrete monolithic algorithm with P1 P1 stabilized finite elements for the fluid problem; for this alghorithm…

Numerical Analysis · Mathematics 2021-05-27 Michele Annese