相关论文: ARAS: Fully algebraic Two-level domain decompositi…

This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…

In this paper, a two-level additive Schwarz preconditioner is proposed for solving the algebraic systems resulting from the finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that the…

In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…

Schwarz methods use a decomposition of the computational domain into subdomains and need to put boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and…

The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…

In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic…

Unsupervised anomaly detection (AD) aims to train robust detection models using only normal samples, while can generalize well to unseen anomalies. Recent research focuses on a unified unsupervised AD setting in which only one model is…

Solving linear systems is often the computational bottleneck in real-life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a…

The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…

We consider multigrid methods for finite volume discretizations of the Reynolds Averaged Navier-Stokes (RANS) equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such…

Efficient simulation of Darcy flow in highly heterogeneous porous media requires iterative solvers that remain robust under large permeability contrasts and mixed boundary conditions. Spectral coarse spaces in two-level overlapping Schwarz…

Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully parameterized networks. In this paper, RaNNs are integrated…

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

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…

A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…

We consider one-level additive Schwarz domain decomposition preconditioners for the Helmholtz equation with variable coefficients (modelling wave propagation in heterogeneous media), subject to boundary conditions that include wave…

In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…

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…

Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…

Recently, autoregressive (AR) models have shown strong potential in image generation, offering better scalability and easier integration with unified multi-modal systems compared to diffusion-based methods. However, extending AR models to…