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This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the…

Numerical Analysis · Mathematics 2019-10-15 Ana Budisa , Wietse Boon , Xiaozhe Hu

The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…

Numerical Analysis · Mathematics 2019-02-05 Kevin W. Aiton , Tobin A. Driscoll

In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…

Numerical Analysis · Mathematics 2012-12-07 Yury Gryazin

Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for…

Numerical Analysis · Mathematics 2020-04-24 Roman Weinhandl , Peter Benner , Thomas Richter

We develop robust solvers for a class of perturbed saddle-point problems arising in the study of a second-order elliptic equation in mixed form (in terms of flux and potential), and of the four-field formulation of Biot's consolidation…

Numerical Analysis · Mathematics 2020-11-11 Wietse M. Boon , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

We derive an extension of the sequential homotopy method that allows for the application of inexact solvers for the linear (double) saddle-point systems arising in the local semismooth Newton method for the homotopy subproblems. For the…

Optimization and Control · Mathematics 2023-11-30 John W. Pearson , Andreas Potschka

We construct and analyze a preconditioner of the linear elastiity system discretized by conforming linear finite elements in the framework of the auxiliary space method. The auxiliary space preconditioner is based on discretization of a…

Numerical Analysis · Mathematics 2010-03-15 James Brannick , Durkbin Cho

A new preconditioner based on a block $LDU$ factorization with algebraic multigrid subsolves for scalability is introduced for the large, structured systems appearing in implicit Runge-Kutta time integration of parabolic partial…

Numerical Analysis · Mathematics 2021-01-15 Md Masud Rana , Victoria E. Howle , Katharine Long , Ashley Meek , William Milestone

We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using…

Numerical Analysis · Mathematics 2010-05-20 Toni Lassila , Gianluigi Rozza

We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling…

Numerical Analysis · Mathematics 2022-08-03 L. Bergamaschi , M. Ferronato , G. Isotton , C. Janna , A. Martinez

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…

Numerical Analysis · Mathematics 2025-12-02 Filipe Cumaru , Alexander Heinlein , Joachim Schöberl

A block diagonal preconditioner with the minimal residual method and a block triangular preconditioner with the generalized minimal residual method are developed for Hu-Zhang mixed finite element methods of linear elasticity. They are based…

Numerical Analysis · Mathematics 2016-05-24 Long Chen , Jun Hu , Xuehai Huang

In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

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

A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-alpha scheme are used for the spatial and temporal discretization. The membrane…

Computational Physics · Physics 2018-12-31 Roger A. Sauer , Tobias Luginsland

This paper is concerned with the partitioned iterative formulation to simulate the fluid-structure interaction of a nonlinear multibody system in an incompressible turbulent flow. The proposed formulation relies on a three-dimensional (3D)…

Fluid Dynamics · Physics 2019-03-05 P S Gurugubelli , R Ghoshal , V Joshi , R K Jaiman

We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…

Numerical Analysis · Mathematics 2025-09-25 Sabit Mahmood Khan , Yashar Mehmani

We present a block lower triangular (BLT) preconditioner to accelerate the convergence of nthe Krylov subspace iterative methods, such as generalized minimal residual (GMRES), for solving a broad class of complex symmetric system of linear…

Numerical Analysis · Mathematics 2016-11-14 Davod Khojasteh Salkuyeh , Tahereh Salimi Siahkalaei

We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods.…

Numerical Analysis · Mathematics 2024-01-11 Alena Kopaničáková , George Em Karniadakis