相关论文: Tridiagonal and Block Tridiagonal computed Sparse …

We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017].…

In the present study, we consider the Extra-Membrane-Intra model (EMI) for the simulation of excitable tissues at the cellular level. We provide the (possibly large) system of partial differential equations (PDEs), equipped with ad hoc…

We present preconditioning techniques to solve linear systems of equations with a block two-by-two and three-by-three structure arising from finite element discretizations of the fictitious domain method with Lagrange multipliers. In…

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…

A hierarchical quasi-Helmholtz decomposition, originally developed to address the low-frequency and dense-discretization breakdowns for the EFIE, is applied together with an algebraic preconditioner to improve the convergence of the CFIE in…

We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling…

Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid…

We present and analyze a preconditioner of the additive Schwarz type for the mortar boundary element method. As a basic splitting, on each subdomain we separate the degrees of freedom related to its boundary from the inner degrees of…

Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, standard approaches can fail to provide scalable approximation…

This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase…

We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with…

This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about…

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…

Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…

Here we consider the factorized sparse approximate inverse (FSAI) preconditioner. We apply the FSAI preconditioner to singular irreducible M-matrices. These matrices arise e.g. in discrete Markov chain modeling or as graph Laplacians. We…

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…

We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is…

We propose and analyze an overlapping Schwarz preconditioner for the $p$ and $hp$ boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is…

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…