相关论文: Symbol-based multilevel block $\tau$ preconditione…

In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…

In this work, we propose and study a preconditioned framework with a graphic Ginzburg-Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge…

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear…

We propose and analyze a general framework called nonlinear preconditioned primal-dual with projection for solving nonconvex-nonconcave and non-smooth saddle-point problems. The framework consists of two steps. The first is a nonlinear…

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of space-time fractional advection-diffusion equations. To start with, an implicit method based on two-sided Gr\"unwald formulae is…

In this paper, fast numerical methods are established for solving a class of time distributed-order and Riesz space fractional diffusion-wave equations. We derive new difference schemes by the weighted and shifted Gr$\ddot{\rm{u}}$nwald…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…

When only few data samples are accessible, utilizing structural prior knowledge is essential for estimating covariance matrices and their inverses. One prominent example is knowing the covariance matrix to be Toeplitz structured, which…

Use of the stochastic Galerkin finite element methods leads to large systems of linear equations obtained by the discretization of tensor product solution spaces along their spatial and stochastic dimensions. These systems are typically…

ILU(k) is a commonly used preconditioner for iterative linear solvers for sparse, non-symmetric systems. It is often preferred for the sake of its stability. We present TPILU(k), the first efficiently parallelized ILU(k) preconditioner that…

We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…

In this paper, the generalized shift-splitting preconditioner is implemented for saddle point problems with symmetric positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block. The proposed preconditioner is extracted…

In this work, we perform a spectral analysis of flipped multilevel Toeplitz sequences, i.e., we study the asymptotic spectral behaviour of $\{Y_{\boldsymbol{n}}T_{\boldsymbol{n}}(f)\}_{\boldsymbol{n}}$, where $T_{\boldsymbol{n}}(f)$ is a…

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…

An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time…

In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…

In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…

As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…