Abstract Domain decomposition (DD) is a powerful approach to numerically solve partial
differential equations, and it has become popular and indispensable in simulations of fluid …

Conduits, the main channels within a rock mass, can significantly affect the permeability
characteristics of rock masses. This paper presents a Stokes–Brinkman–Darcy coupling …

The aim of this paper is to study a stationary Brinkman problem in an anisotropic porous
medium by using a mini-element method with a general boundary condition. One of the …

This work describes the development of matrix-free GPU-accelerated solvers for high-order
finite element problems in. The solvers are applicable to grad-div and Darcy problems in …

Natural heat convection, mixed heat convection and heat transfer by conduction and
convection with solidification of a ternary alloy are described by the finite volume method …

The balancing domain decomposition by constraints methods (BDDC) have been applied to
solve the saddle point problem arising from a hybridizable discontinuous Galerkin (HDG) …

Hydrodynamics characterization and analysis is an essential part in studying mineral
dissolution in porous media with complex heterogeneous pore structures including …

We discuss the efficient implementation of powerful domain decomposition smoothers for
multigrid methods for high-order discontinuous Galerkin (DG) finite element methods. In …

In this paper, we present a geometric multigrid methodology for the solution of matrix
systems associated with isogeometric compatible discretizations of the generalized Stokes …

A strongly symmetric stress approximation is proposed for the Brinkman equations with
mixed boundary conditions. The resulting formulation solves for the Cauchy stress using a …