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In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

Computational Engineering, Finance, and Science · Computer Science 2024-12-20 Santiago Badia , Alberto F. Martín , Marc Olm

In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…

Numerical Analysis · Mathematics 2025-05-26 Jun Li , Lingsheng Meng

We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…

Numerical Analysis · Mathematics 2023-09-29 Monica Montardini , Giancarlo Sangalli , Mattia Tani

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

We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…

Numerical Analysis · Mathematics 2019-03-07 Ulrich Langer , Andreas Schafelner

We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the…

Numerical Analysis · Mathematics 2016-05-25 Ulrich Langer , Stephen E. Moore , Martin Neumüller

We present a novel multiscale numerical approach that combines parallel-in-time computation with hybrid domain adaptation for linear collisional kinetic equations in the diffusive regime. The method addresses the computational challenges of…

Numerical Analysis · Mathematics 2025-11-18 Tino Laidin

In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…

Numerical Analysis · Mathematics 2019-06-26 Fanhai Zeng , Ian Turner , Kevin Burrage , Stephen J. Wright

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…

Numerical Analysis · Mathematics 2024-03-29 Margherita Guido , Daniel Kressner , Paolo Ricci

The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system at each time-step. This work develops a fully robust and…

Numerical Analysis · Mathematics 2025-01-29 Iain Smears

Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…

Numerical Analysis · Mathematics 2021-03-05 Stefan Takacs

Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…

Numerical Analysis · Mathematics 2022-01-04 Hussam Al Daas , Pierre Jolivet , Jennifer Scott

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued…

Numerical Analysis · Mathematics 2011-11-01 Blanca Ayuso de Dios , Ivan Georgiev , Johannes Kraus , Ludmil Zikatanov

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

We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…

Numerical Analysis · Mathematics 2017-08-22 Clemens Hofreither , Stefan Takacs

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Numerical Analysis · Mathematics 2021-12-24 Jennifer Scott , Miroslav Tuma

LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these…

Numerical Analysis · Mathematics 2024-08-30 Mei Yang , Gul Karaduman , Ren-Cang Li

We present and analyze a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic evolution equations in moving space-time computational domains. Following…

Numerical Analysis · Mathematics 2017-07-27 Stephen Edward Moore

In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…

Numerical Analysis · Mathematics 2023-06-29 Matthias Bolten , Scott P. MacLachlan , Misha E. Kilmer

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…

Numerical Analysis · Mathematics 2023-01-23 Santiago Badia , Hridya Dilip , Francesc Verdugo