Related papers: Hybridised multigrid preconditioners for a compati…
We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject…
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…
Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points.…
In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of…
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations…
The reformulation of the Met Office's dynamical core for weather and climate prediction previously described by the authors is extended to spherical domains using a cubed-sphere mesh. This paper updates the semi-implicit mixed…
We develop a fully discrete, semi-implicit mixed finite element method for approximating solutions to a class of fourth-order stochastic partial differential equations (SPDEs) with non-globally Lipschitz and non-monotone nonlinearities,…
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…
This paper concerns the preconditioning technique for discrete systems arising from time-harmonic Maxwell equations with absorptions, where the discrete systems are generated by N\'ed\'elec finite element methods of fixed order on meshes…
In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…
This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully…
A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…
A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
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 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…
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…