相关论文: Preconditioning of Active-Set Newton Methods for P…

We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…

In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…

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…

In this paper, a novel augmented Lagrangian preconditioner based on global Arnoldi for accelerating the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure, these systems…

We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…

In this paper, we propose a generalized shift-splitting (GSS) preconditioner, along with its two relaxed variants to solve the double saddle point problem (DSPP). The convergence of the associated GSS iterative method is analyzed, and…

The Newton's method for solving stationary Navier-Stokes equations (NSE) is known to convergent fast, however, may fail due to a bad initial guess. This work presents a simple-to-implement nonlinear preconditioning of Newton's iteration,…

This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…

We derive eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with block-diagonal Schur complement matrices. This analysis applies to an arbitrary number of blocks and accounts for the case where…

For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…

Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…

Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…

In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…

In this paper, we execute the shift-splitting preconditioner for asymmetric saddle point problems with its (1,2) block's transposition unequal to its (2,1) block under the removed minus of its (2,1) block. The proposed preconditioner is…

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury…

We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…