Related papers: hr-adaptivity for nonconforming high-order meshes …
Hierarchical matrices are data-sparse approximations of dense matrices that are widely used for fast matrix computations. Hierarchical matrices are built using a tree data structure, with low-rank blocks identified by various admissibility…
It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently…
Magnetic soft robots embedded with hard magnetic particles enable untethered actuation via external magnetic fields, offering remote, rapid, and precise control, which is highly promising for biomedical applications. However, designing such…
This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
Complex non-local behavior makes designing high efficiency and multifunctional metasurfaces a significant challenge. While using libraries of meta-atoms provide a simple and fast implementation methodology, pillar to pillar interaction…
Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…
The design of porous infill structures presents significant challenges due to their complex geometric configurations, such as the accurate representation of geometric boundaries and the control of localized maximum stress. In current…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
This paper develops a unified high-order accumulative regularization (AR) framework for convex and uniformly convex gradient norm minimization. Existing high-order methods often exhibit a gap: the function-value residual decreases fast,…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
Optical proximity correction (OPC) is a widely-used resolution enhancement technique (RET) for printability optimization. Recently, rigorous numerical optimization and fast machine learning are the research focus of OPC in both academia and…
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…
We propose and analyse a fully adaptive strategy for solving elliptic PDEs with random data in this work. A hierarchical sequence of adaptive mesh refinements for the spatial approximation is combined with adaptive anisotropic sparse…
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…
This paper introduces ItsOPT, an inexact two-level smoothing optimization framework designed to find first-order critical points of nonsmooth and nonconvex functions. The framework involves two levels of methodologies: at the upper level, a…
An extension of the multi-level hp Finite Cell Method is proposed for the simulation of thermoviscoplastic problems with temperature-dependent material behavior. The approach combines hierarchical adaptive refinement with a non-negative…
Soft robotics has emerged as the standard solution for grasping deformable objects, and has proven invaluable for mobile robotic exploration in extreme environments. However, despite this growth, there are no widely adopted computational…
Target-oriented discovery under limited evaluation budgets requires making reliable progress in high-dimensional, heterogeneous design spaces where each new measurement is costly, whether experimental or high-fidelity simulation. We present…
Machine learning has achieved remarkable success over the past couple of decades, often attributed to a combination of algorithmic innovations and the availability of high-quality data available at scale. However, a third critical component…