相关论文: A power Schur complement Low-Rank correction preco…

We present a hierarchical basis preconditioning strategy for the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering both simply and multiply connected geometries.To this end, we first consider the direct…

Models in which the covariance matrix has the structure of a sparse matrix plus a low rank perturbation are ubiquitous in data science applications. It is often desirable for algorithms to take advantage of such structures, avoiding costly…

We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of…

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…

With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are…

Incomplete LU factorizations of sparse matrices are widely used as preconditioners in Krylov subspace methods to speed up solving linear systems. Unfortunately, computing the preconditioner itself can be time-consuming and sensitive to…

If the Stokes equations are properly discretized, it is known that the Schur complement matrix is spectrally equivalent to the identity matrix. Moreover, in the case of simple geometries, it is often observed that most of its eigenvalues…

Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…

A symmetric and a nonsymmetric variant of the additive Schwarz preconditioner are proposed for the solution of a nonsymmetric system of algebraic equations arising from a general finite volume element discretization of symmetric elliptic…

We consider the numerical solution of large scale time-harmonic Maxwell equations. To this day, this problem remains difficult, in particular because the equations are neither Hermitian nor semi-definite. Our approach is to compare…

Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…

The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…

The aim of this paper is to solve large-and-sparse linear Semidefinite Programs (SDPs) with low-rank solutions. We propose to use a preconditioned conjugate gradient method within second-order SDP algorithms and introduce a new efficient…

We consider an iterative eigensolver for Schr\"odinger equations that constructs low-rank approximations of eigenfunctions with accuracy-adapted ranks, with particular focus on fermionic Schr\"odinger equations in second-quantized form and…

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and…

We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…

In this paper, we propose a parameter-robust preconditioner for the coupled Stokes-Darcy problem equipped with various boundary conditions, enforcing the mass conservation at the interface via a Lagrange multiplier. We rigorously establish…

Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…

We show that the mass matrix derived from finite elements can be effectively used as a preconditioner for iteratively solving the linear system arising from finite-difference discretization of the Poisson equation, using the conjugate…