相关论文: Weighted BFBT Preconditioner for Stokes Flow Probl…

A two-step preconditioned iterative method based on the Hermitian/Skew-Hermitian splitting is applied to the solution of nonsymmetric linear systems arising from the Finite Element approximation of convection-diffusion equations. The…

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

We develop two unfitted finite element methods for the Stokes equations using $H^{\text{div}}$-conforming finite elements. Both methods achieve optimal convergence for velocity, ensure pointwise divergence-free velocity fields, and produce…

We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the…

We develop $H$(div)-conforming mixed finite element methods for the unsteady Stokes equations modeling single-phase incompressible fluid flow. A projection method in the framework of the incremental pressure correction methodology is…

A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the…

We consider block preconditioners for double saddle-point systems, and investigate the effect of approximating the nested Schur complement associated with the trailing diagonal block on the eigenvalue distribution of the preconditioned…

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement…

In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a…

A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A…

A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it…

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…

We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems…

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…

In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…

This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The…

This article proposes modifications to standard low order finite element approximations of the Stokes system with the goal of improving both the approximation quality and the parallel algebraic solution process. Different from standard…

We develop a linearly-scaling variant of the Force Coupling Method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly-periodic geometry with either a…

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…

The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender…