相关论文: Sparsifying preconditioner for the time-harmonic M…

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…

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…

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…

We investigate the SPAI and PSAI preconditioning procedures and shed light on two important features of them: (i) For the large linear system $Ax=b$ with $A$ irregular sparse, i.e., with $A$ having $s$ relatively dense columns, SPAI may be…

We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…

We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, the discretized equations are solved with a preconditioned…

This paper addresses the structurally-constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal…

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…

Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically…

For a class of ergodic parabolic semilinear stochastic partial differential equations (SPDEs) with gradient structure, we introduce a preconditioning technique and design high-order integrators for the approximation of the invariant…

In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…

In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for…

In this work the Lippmann-Schwinger equation is used to model seismic waves in strongly scattering acoustic media. We consider the Helmholtz equation, which is the scalar wave equation in the frequency domain with constant density and…

The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta…

The PMCHWT integral equation enables the modelling of scattering of time-harmonic fields by penetrable, piecewise homogeneous, systems. They have been generalised to include the modelling of composite systems that may contain junctions,…

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…

Our work is about energy conserving fourth-order time discretizations of a three-field formulation of Maxwell's equations in conjunction with a spatial discretization using higher-order and compatible de Rham finite element spaces. Toward…