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