相关论文: A unified error analysis of HDG methods for the st…

We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…

For nonexpansive fixed-point problems, Halpern's method with optimal parameters, its so-called H-dual algorithm, and in fact, an infinite family of algorithms containing them, all exhibit the exactly minimax optimal convergence rates. In…

This paper investigates the convergence properties of the hypergradient descent method (HDM), a 25-year-old heuristic originally proposed for adaptive stepsize selection in stochastic first-order methods. We provide the first rigorous…

Algebraic Multigrid (AMG) methods have been proven to be effective solvers for large-scale linear algebraic systems $Ax = b$ with Hermitian positive definite (HPD) matrix $A$. For such problems the convergence in the $A$-norm is well…

We propose and analyze two a posteriori error indicators for hybridizable discontinuous Galerkin (HDG) discretizations of the Helmholtz equation. These indicators are built to minimize the residual associated with a local superconvergent…

This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by…

Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization…

This paper introduces a unified analysis framework of equal-order hybridized discontinuous finite element (HDG) methods. The general framework covers standard HDG, embedded discontinuous finite element, and embedded-hybridized discontinuous…

A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two…

For a generalized Hodge Laplace equation, we prove the quasi-optimal convergence rate of an adaptive mixed finite element method. This adaptive method can control the error in the natural mixed variational norm when the space of harmonic…

This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The…

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…

Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence…

The two-fluid plasma model has a wide range of timescales which must all be numerically resolved regardless of the timescale on which plasma dynamics occurs. The answer to solving numerically stiff systems is generally to utilize…

Gaussian radial basis functions can be an accurate basis for multivariate interpolation. In practise, high accuracies are often achieved in the flat limit where the interpolation matrix becomes increasingly ill-conditioned. Stable…

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…

This work proposes a unified $hp$-adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs' type. In particular, we present unified $hp$-HDG…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…