Related papers: Adaptive Mesh Refinement and Error Estimation Meth…
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…
Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical $r$-adaptivity optimizes vertex positions but requires solving expensive auxiliary PDEs…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
Accurately estimating the pose of an object is a crucial task in computer vision and robotics. There are two main deep learning approaches for this: geometric representation regression and iterative refinement. However, these methods have…
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to…
We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…
In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing…
Direct collocation methods are widely used numerical techniques for solving optimal control problems. The discretization of continuous-time optimal control problems transforms them into large-scale nonlinear programming problems, which…
Whether is ground-based or space-based, any optical instrument suffers from some amount of optical geometric distortion. Recently, the diffraction-limited image quality afforded by space-based telescopes and by Adaptive Optics (AO)…
Numerical evolution of the spherically symmetric, massive Klein-Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system…
We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…
Discrete and mixed-variable optimization problems have appeared in several real-world applications. Most of the research on mixed-variable optimization considers a mixture of integer and continuous variables, and several integer handlings…
Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…
The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically,…