相关论文: Optimality of multilevel preconditioners for local…

We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local $h$-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is…

We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It…

We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…

We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…

B* is a novel optimization framework that addresses a critical challenge in fixed-base manipulator robotics: optimal base placement. Current methods rely on pre-computed kinematics databases generated through sampling to search for…

Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…

This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…

We present an $n$-dimensional marked bisection method for unstructured conformal meshes. We devise the method for local refinement in adaptive $n$-dimensional applications. To this end, we propose a mesh marking pre-process and three marked…

PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…

This paper considers optimization of smooth nonconvex functionals in smooth infinite dimensional spaces. A H\"older gradient descent algorithm is first proposed for finding approximate first-order points of regularized polynomial…

We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…

Proximal gradient methods are a popular tool for the solution of structured, nonsmooth minimization problems. In this work, we investigate an extension of the former to general Banach spaces and provide worst-case convergence rates for,…

In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under…

In this work we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent, Gradient Clipping and Adam. We consider preconditioners of the form $\nabla K$,…

We present a variational multi-label segmentation algorithm based on a robust Huber loss for both the data and the regularizer, minimized within a convex optimization framework. We introduce a novel constraint on the common areas, to bias…

Artificial intelligence can rapidly propose candidate phases and structures from X-ray diffraction (XRD), but these hypotheses often fail in downstream refinement because peak intensities cannot be stably assigned under severe overlap and…

The block structure of double saddle-point problems has prompted extensive research into efficient preconditioners. This paper introduces a novel class of three-by-three block preconditioners tailored for such systems from the…

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…

In this work, we construct high-order finite element spaces for the $L^2$ de Rham complex on triangular meshes amenable to low-order-refined preconditioning. The spaces are constructed using the Duffy transformation, by pulling back…