English
Related papers

Related papers: Error Analysis for Quadtree-Type Mesh-Coarsening A…

200 papers

Compressed sensing is an image reconstruction technique to achieve high-quality results from limited amount of data. In order to achieve this, it utilizes prior knowledge about the samples that shall be reconstructed. Focusing on image…

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…

Numerical Analysis · Mathematics 2026-02-26 Vladimír Lukeš , Eduard Rohan

This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…

Numerical Analysis · Mathematics 2026-03-19 Hou Man , Chongmin Song , Sundararajan Natarajan , Ean Tat Ooi , Carolin Birk

This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…

Numerical Analysis · Mathematics 2023-03-31 Daniel van Huyssteen , Felipe Lopez Rivarola , Guillermo Etse , Paul Steinmann

Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…

Mathematical Software · Computer Science 2024-01-30 Ketan Mittal , Veselin A. Dobrev , Patrick Knupp , Tzanio Kolev , Franck Ledoux , Claire Roche , Vladimir Z. Tomov

In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…

Computer Vision and Pattern Recognition · Computer Science 2025-09-09 Anuraag Mishra , Andrea Gilch , Benjamin Apeleo Zubiri , Jan Rolfes , Frauke Liers

The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces…

Numerical Analysis · Mathematics 2023-04-05 Michael Feischl , Hubert Hackl

We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…

Computational Physics · Physics 2025-12-19 Furkan Şık , F. L. Teixeira , B. Shanker

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

Numerical Analysis · Mathematics 2021-09-01 Santiago Badia , Manuel Caicedo , Alberto F. Martín , Javier Principe

As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation…

Computer Vision and Pattern Recognition · Computer Science 2020-07-20 Karrar Abbas , Xianping Li

There has been significant progress in Masked Image Modeling (MIM). Existing MIM methods can be broadly categorized into two groups based on the reconstruction target: pixel-based and tokenizer-based approaches. The former offers a simpler…

Computer Vision and Pattern Recognition · Computer Science 2023-08-02 Yuan Liu , Songyang Zhang , Jiacheng Chen , Zhaohui Yu , Kai Chen , Dahua Lin

Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the…

Machine Learning · Computer Science 2022-07-25 Joseph G. Wallwork , Jingyi Lu , Mingrui Zhang , Matthew D. Piggott

Understanding the applicability and limitations of electronic-structure methods needs careful and efficient comparison with accurate reference data. Knowledge of the quality and errors of electronic-structure calculations is crucial to…

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

Numerical Analysis · Mathematics 2021-06-15 Cale Harnish , Luke Dalessandro , Karel Matous , Daniel Livescu

Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…

Graphics · Computer Science 2026-05-07 Xuan Wang , Zhaofeng Luo , Minchen Li , Taku Komura , Kemeng Huang

We present a robust and efficient target-based mesh adaptation methodology, building on hybridized discontinuous Galerkin schemes for (nonlinear) convection-diffusion problems, including the compressible Euler and Navier-Stokes equations.…

Numerical Analysis · Mathematics 2014-11-12 Michael Woopen , Georg May , Jochen Schütz

Significant developments in the field of additive manufacturing (AM) allowed the fabrication of complex microarchitectured components with varying porosity across different scales. However, due to the high complexity of this process, the…

Computational Engineering, Finance, and Science · Computer Science 2020-12-16 N. Korshunova , J. Jomo , G. Lékó , D. Reznik , P. Balázs , S. Kollmannsberger

Image segmentation is fundamental to microstructural analysis for defect identification and structure-property correlation, yet remains challenging due to pronounced heterogeneity in materials images arising from varied processing and…

Computer Vision and Pattern Recognition · Computer Science 2026-03-17 Sanjeev S. Navaratna , Nikhil Thawari , Gunashekhar Mari , Amritha V P , Murugaiyan Amirthalingam , Rohit Batra

Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…

Soft Condensed Matter · Physics 2020-04-16 Ondřej Rokoš , Jan Zeman , Martin Doškář , Petr Krysl

We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…

Numerical Analysis · Mathematics 2025-07-03 Tzanio Kolev , Boyan Lazarov , Ketan Mittal , Mathias Schmidt , Vladimir Tomov