Related papers: Effective Preconditioners for Mixed-Dimensional Sc…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
In this paper, the authors constructed an auxiliary space multigrid preconditioner for the weak Galerkin finite element method for second-order diffusion equations, discretized on simplicial 2D or 3D meshes. The idea of the auxiliary space…
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…
Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the…
In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several preconditioners for the classical three-filed Biot model under the…
A discretization scheme for variable coefficient elliptic PDEs in the plane is presented. The scheme is based on high-order Gaussian quadratures and is designed for problems with smooth solutions, such as scattering problems involving soft…
The numerical modeling of fracture contact thermo-poromechanics is crucial for advancing subsurface engineering applications, including CO2 sequestration, production of geo-energy resources, energy storage and wastewater disposal…
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…
We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient…
In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…
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…
The paper is devoted to the spectral analysis of effective preconditioners for linear systems obtained via a Finite Element approximation to diffusion-dominated convection-diffusion equations. We consider a model setting in which the…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are…
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…
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…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…
In this work, we propose a robust and easily implemented algebraic multigrid method as a stand-alone solver or a preconditioner in Krylov subspace methods for solving either symmetric and positive definite or saddle point linear systems of…
In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the second order elliptic equations. The preconditioners are…