Related papers: Fast and flexible preconditioners for solving mult…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
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…
Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning (FASP), we develop efficient and user-friendly multilevel…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…
In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…
The discretization of the double-layer potential integral equation for the interior Dirichlet Laplace problem in a domain with smooth boundary results in a linear system that has a bounded condition number. Thus, the number of iterations…
Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…
Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…
We derive a linearized rotating shallow water system modeling tides, which can be discretized by mixed finite elements. Unlike previous models, this model allows for multiple layers stratified by density. Like the single-layer…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…
Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…
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 propose a preconditioner based on the shift-splitting method for generalized saddle point problems with nonsymmetric positive definite (1,1)-block and symmetric positive semidefinite $(2,2)$-block. The proposed…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
Implicit solvers for atmospheric models are often accelerated via the solution of a preconditioned system. For block preconditioners this typically involves the factorisation of the (approximate) Jacobian resulting from linearization of the…