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The solution of matrices with $2\times 2$ block structure arises in numerous areas of computational mathematics, such as PDE discretizations based on mixed-finite element methods, constrained optimization problems, or the implicit or steady…

Numerical Analysis · Mathematics 2023-07-07 Ben S. Southworth , Abdullah A. Sivas , Sander Rhebergen

We develop an enclosure-type reconstruction scheme to identify penetrable and impenetrable obstacles in electromagnetic field with anisotropic medium in \mathbb{R}^{3}. The main difficulty in treating this problem lies in the fact that…

Analysis of PDEs · Mathematics 2015-01-20 Rulin Kuan , Yi-Hsuan Lin , Mourad Sini

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…

Numerical Analysis · Mathematics 2021-02-03 Xiaoqiang Yue , Shulei Zhang , Xiaowen Xu , Shi Shu , Weidong Shi

This is the third part in a series on a mass conserving, high order, mixed finite element method for Stokes flow. In this part, we study a block-diagonal preconditioner for the indefinite Schur complement system arising from the…

Numerical Analysis · Mathematics 2021-09-30 Mark Ainsworth , Charles Parker

The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic…

Numerical Analysis · Mathematics 2014-04-08 Pierre Degond , Fabrice Deluzet , Alexei Lozinski , Jacek Narski , Claudia Negulescu

Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution…

Optimization and Control · Mathematics 2020-07-14 Rien Quirynen , Stefano Di Cairano

Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional…

Numerical Analysis · Mathematics 2023-02-08 Xiaozhe Hu , Eirik Keilegavlen , Jan M. Nordbotten

In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block…

Numerical Analysis · Mathematics 2016-06-22 Yicong Ma , Kaibo Hu , Xiaozhe Hu , Jinchao Xu

This paper presents a scalable physics-based block preconditioner for mixed-dimensional models in beam-solid interaction and their application in engineering. In particular, it studies the linear systems arising from a regularized…

Computational Engineering, Finance, and Science · Computer Science 2024-08-09 Max Firmbach , Ivo Steinbrecher , Alexander Popp , Matthias Mayr

In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of…

Optimization and Control · Mathematics 2024-07-17 Chaojie Wang

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy…

Numerical Analysis · Mathematics 2025-12-01 Domenico Caparello , Lorenzo Pareschi , Thomas Rey

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…

Numerical Analysis · Mathematics 2025-10-20 Erik Boman , Bruce Hendrickson , Stephen Vavasis

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

Numerical Analysis · Mathematics 2023-10-26 Fatemeh P. A. Beik , Michele Benzi

Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this process is modeled by a nonlinear system of partial differential…

Numerical Analysis · Mathematics 2018-01-26 Quan M. Bui , Howard C. Elman , J. D. Moulton

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods. The high-order…

Numerical Analysis · Mathematics 2021-03-11 Will Pazner

This work investigates inexact block Schur complement preconditioning for linear poroelasticity problems discretized using a hybrid approach: Bernardi-Raugel elements for solid displacement and lowest-order weak Galerkin elements for fluid…

Numerical Analysis · Mathematics 2025-12-25 Weizhang Huang , Zhuoran Wang

In this study, a novel preconditioner based on the absolute-value block $\alpha$-circulant matrix approximation is developed, specifically designed for nonsymmetric dense block lower triangular Toeplitz (BLTT) systems that emerge from the…

Numerical Analysis · Mathematics 2023-12-22 Congcong Li , Xuelei Lin , Sean Hon , Shu-Lin Wu

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…

Numerical Analysis · Mathematics 2021-09-06 Davod Khojasteh Salkuyeh

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…

Numerical Analysis · Mathematics 2021-09-13 Hamed Aslani , Davod Khojasteh Salkuyeh , Fatemeh Panjeh Ali Beik

In this paper, a new asymptotic preserving (AP) scheme is proposed for the anisotropic elliptic equations. Different from previous AP schemes, the actual one is based on first-order system least-squares for second-order partial differential…

Numerical Analysis · Mathematics 2022-02-09 Long Li , Chang Yang