Related papers: A Symmetric Multigrid-Preconditioned Krylov Subspa…
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 novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…
We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces…
Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the resulting linear and nonlinear systems. In this work, we…
The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. One such strategy is multigrid. To realize the potential of…
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations in isogeometric analysis and have proven that the convergence…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
Motivated by the need for efficient and accurate simulation of the dynamics of the polar ice sheets, we design high-order finite element discretizations and scalable solvers for the solution of nonlinear incompressible Stokes equations. We…
In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast…
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…
This work presents a multigrid preconditioned high order immersed finite difference solver to accurately and efficiently solve the Poisson equation on complex 2D and 3D domains. The solver employs a low order Shortley-Weller multigrid…
In this study, we present an $hp$-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming…
Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…
This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…
This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…
Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development…
The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, the location/values of the applied Dirichlet/Neumann boundary…