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For the solution of discrete ill-posed problems, in this paper a novel preconditioned iterative method based on the Arnoldi algorithm for matrix functions is presented. The method is also extended to work in connection with Tikhonov…

Numerical Analysis · Mathematics 2011-11-18 Paolo Novati , Michela Redivo-Zaglia , Maria Rosaria Russo

We consider the use of multipreconditioning to solve linear systems when more than one preconditioner is available but the optimal choice is not known. In particular, we consider a selective multipreconditioned GMRES algorithm where we…

Numerical Analysis · Mathematics 2021-07-08 Niall Bootland , Andrew Wathen

A new domain decomposition preconditioner is introduced for efficiently solving linear systems Ax = b with a symmetric positive definite matrix A. The particularity of the new preconditioner is that it is not necessary to have access to the…

Numerical Analysis · Mathematics 2021-06-23 Nicole Spillane

This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the Lippmann-Schwinger equation, this paper generalizes that…

Numerical Analysis · Mathematics 2018-11-14 Fei Liu , Lexing Ying

The novel contribution of this paper relies in the proposal of a fully implicit numerical method designed for nonlinear degenerate parabolic equations, in its convergence/stability analysis, and in the study of the related computational…

Numerical Analysis · Mathematics 2010-01-20 Matteo Semplice , Marco Donatelli , Stefano Serra-Capizzano

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Numerical Analysis · Mathematics 2019-07-08 Ashish Kumar Nandi , Jajati Keshari Sahoo , Debasisha Mishra

This paper presents fast solvers for linear systems arising from the discretization of fractional nonlinear Schr\"odinger equations with Riesz derivatives and attractive nonlinearities. These systems are characterized by complex symmetry,…

Numerical Analysis · Mathematics 2024-10-07 Chao Chen , Xi Yang , Fei-Yan Zhang

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

Numerical Analysis · Mathematics 2019-08-02 Prosper Torsu

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

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…

Numerical Analysis · Mathematics 2018-03-09 D. Jodlbauer , U. Langer , T. Wick

We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…

Numerical Analysis · Mathematics 2014-04-10 Kenneth L. Ho , Leslie Greengard

An adapted deflation preconditioner is employed to accelerate the solution of linear systems resulting from the discretization of fracture mechanics problems with well-conditioned extended/generalized finite elements. The deflation space…

Computational Engineering, Finance, and Science · Computer Science 2022-05-11 Konstantinos Agathos , Tim Dodwell , Eleni Chatzi , Stephane P. A. Bordas

A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…

Numerical Analysis · Mathematics 2026-01-05 Andrew V. Terekhov

In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver…

Numerical Analysis · Mathematics 2016-11-29 Qiya Hu , Shaoliang Hu

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.…

Optimization and Control · Mathematics 2024-03-05 Xueyi Bu , Brian Plancher

The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…

Numerical Analysis · Mathematics 2025-04-08 Andy Wathen

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

Numerical Analysis · Mathematics 2026-05-29 Yonghan Sun , Hou-Duo Qi , Deren Han , Jiaxin Xie

In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed…

Numerical Analysis · Mathematics 2016-08-24 Francesc Verdugo , Wolfgang A. Wall

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

Numerical Analysis · Mathematics 2020-06-25 Miguel Zambrano , Sintya Serrano , Boyan S. Lazarov , Juan Galvis

To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…

Computational Physics · Physics 2023-05-16 Ling-Ze Bu , Wei Wang