相关论文: Analysis of block-preconditioners for models of co…

For a prescribed porosity, the coupled magma/mantle flow equations can be formulated as a two-field system of equations with velocity and pressure as unknowns. Previous work has shown that while optimal preconditioners for the two-field…

We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze…

The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now…

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…

In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. The discretization is proved to be well-posed with respect to the physical and discretization parameters, and…

We have presented a fast method for solving a specific type of block four-by-four saddlepoint problem arising from the finite element discretization of the generalized 3D Stokes problem. We analyze the eigenvalue distribution and the…

We study the performance of a new block preconditioner for a class of $3\times3$ block saddle point problems which arise from finite element methods for solving time-dependent Maxwell equations and some other practical problems. We also…

Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…

We are studying the efficient solution of the system of linear equation stemming from the mass conserving mixed stress (MCS) method discretization of the Stokes equations. To that end we perform static condensation to arrive at a system for…

We derive parameter-robust quasi-optimal error estimates for mixed finite element methods for the nonlinear Darcy--Forchheimer equations with mixed boundary conditions. Using the framework of operator preconditioning, we also design…

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations. Galerkin discretizations of the classical Poggio-Miller-Chang-Harrington-Wu-Tsai…

We present a model problem for benchmarking codes that investigate magma migration in the Earth's interior. This system retains the essential features of more sophisticated models, yet has the advantage of possessing solitary wave…

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes-Darcy problem. Three different formulations and their discretizations in terms of conforming and non-conforming finite element methods and…

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 design robust and efficient linear solvers for the numerical approximation of solutions to Maxwell's equations with dissipative boundary conditions. We consider a structure-preserving finite-element approximation with…

Due to the indefiniteness and poor spectral properties, the discretized linear algebraic system of the vector Laplacian by mixed finite element methods is hard to solve. A block diagonal preconditioner has been developed and shown to be an…

We study the iterative solution of linear systems of equations arising from stochastic Galerkin finite element discretizations of saddle point problems. We focus on the Stokes model with random data parametrized by uniformly distributed…

We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-dependent problems which are discretized using backward Euler or…

We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…