Related papers: AMBER: Adaptive Mesh Generation by Iterative Mesh …
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive…
We present here the result of continuation work, performed to further fulfill the vision we outlined in [Harel,Lekien,P\'eba\"y-2017] for the visualization and analysis of tree-based adaptive mesh refinement (AMR) simulations, using the…
Image segmentation is a crucial task in computer vision, with wide-ranging applications in industry. The Segment Anything Model (SAM) has recently attracted intensive attention; however, its application in industrial inspection,…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
Efficiently digitizing high-fidelity animatable human avatars from videos is a challenging and active research topic. Recent volume rendering-based neural representations open a new way for human digitization with their friendly usability…
Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over…
Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over…
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…
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.…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
Adaptive mesh refinement (AMR) is a classical technique about local refinement in space where needed, thus effectively reducing computational costs for HPC-based physics simulations. Although AMR has been used for many years, little…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…
As an entry for the 2001 Gordon Bell Award in the "special" category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) code, Enzo, designed for high-resolution, multiphysics, cosmological structure formation simulations. Our…