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Krylov Subspace Solvers and Preconditioners [PDF]
ESAIM: Proceedings and Surveys, 2018 In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved.
Vuik C.
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A Parallel Solver for FSI Problems with Fictitious Domain Approach
Mathematical and Computational Applications, 2023 We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier–Stokes equations, while the solid
Daniele Boffi +3 more
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Parallel Multilevel Preconditioners [PDF]
Mathematics of Computation, 1990 In this paper, we provide techniques for the development and analysis of parallel multilevel preconditioners for the discrete systems which arise in numerical approximation of symmetric elliptic boundary value problems. These preconditioners are defined as a sum of independent operators on a sequence of nested subspaces of the full approximation space.
Bramble, J.H. +2 more
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Support-Graph Preconditioners [PDF]
SIAM Journal on Matrix Analysis and Applications, 2006 The authors extend the ``support-graph preconditioning'' technique, introduced by \textit{Y. Notay} [Lect. Notes Math. 1457, 105--125 (1990; Zbl 0722.65012); Linear Algebra 154--156, 711--722 (1991; Zbl 0735.65028); Appl. Numer. Math. 10, No. 5, 381--396 (1992; Zbl 0756.65049)], \textit{R. Beauwens} [Linear Algebra Appl.
Bern, Marshall +4 more
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Robust preconditioners for a new stabilized discretization of the poroelastic equations [PDF]
, 2020 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 thus provides a ...
Adler, James H. +5 more
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Reusing Preconditioners in Projection Based Model Order Reduction Algorithms
IEEE Access, 2020 Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension.
Navneet Pratap Singh, Kapil Ahuja
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Applied Sciences, 2023 A Jacobian-free Newton–Krylov (JFNK) method with effective preconditioning strategies is introduced to solve a diffusion-based tumor growth model, also known as the Fisher–Kolmogorov partial differential equation (PDE). The time discretization of the PDE
Samet Y. Kadioglu, Ersin Ozugurlu
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Preconditioning of fully implicit Runge-Kutta schemes for parabolic PDEs [PDF]
Modeling, Identification and Control, 2006 Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs (9).
Gunnar A. Staff +2 more
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Three effective preconditioners for double saddle point problem
AIMS Mathematics, 2021 In this paper, we mainly propose three preconditioners for solving double saddle point problems, which arise from some practical problems. Firstly, the solvability of this kind of problem is investigated under suitable assumption. Next, we prove that all
Yuwen He, Jun Li, Lingsheng Meng
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A Survey of Low-Rank Updates of Preconditioners for Sequences of Symmetric Linear Systems
Algorithms, 2020 The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems A k x k = b k , k = 1 , … arising in many scientific applications, such as ...
Luca Bergamaschi
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