Related papers: A Robust Algebraic Domain Decomposition Preconditi…
We discuss the ill conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson…
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…
The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…
The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element methods. These preconditioners are constructed using…
In this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with $\mathcal{H}^2$-matrices. We propose several new preconditioners…
We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition number minimization problem, under structured transformations…
We introduce a domain decomposition-based nonlinear preconditioned iteration for solving nonlinear, nonsmooth elliptic optimal control problems, with a nonlinear reaction term, $L^1$ regularization and box constraints on the control…
Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage. Modeling this problem accurately presents significant…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
We present a new class of preconditioned iterative methods for solving linear systems of the form $Ax = b$. Our methods are based on constructing a low-rank Nystr\"om approximation to $A$ using sparse random matrix sketching. This…
The Helmholtz wave scattering problem by screens in 2D can be recast into first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introduce two new preconditioners, in the form of square-roots of…
We describe a parallel iterative least squares solver named \texttt{LSRN} that is based on random normal projection. \texttt{LSRN} computes the min-length solution to $\min_{x \in \mathbb{R}^n} \|A x - b\|_2$, where $A \in \mathbb{R}^{m…
Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
Hybridizable discretizations allow for the elimination of local degrees-of-freedom leading to reduced linear systems. In this paper, we determine and analyse an approach to construct parameter-robust preconditioners for these reduced…
Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…
The successive projection algorithm (SPA) can quickly solve a nonnegative matrix factorization problem under a separability assumption. Even if noise is added to the problem, SPA is robust as long as the perturbations caused by the noise…
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…
Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in…