Related papers: Marking strategies for adaptive mesh refinement: A…
In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically…
We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in…
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…
Mixed finite element methods with flux errors in $H(div)$-norms and div-least-squares finite element methods require a separate marking strategy in obligatory adaptive mesh-refining. The refinement indicator $\sigma^2(\mathcal…
We present an improved method for topology optimization with both adaptive mesh refinement and derefinement. Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of…
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive,…
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…
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…
High-order solvers for compressible flows are vital in scientific applications. Adaptive mesh refinement (AMR) is a key technique for reducing computational cost by concentrating resolution in regions of interest. In this work, we develop…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
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…
Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can be used to track discontinuities in the…
Large language models (LLMs) demonstrate strong performance in math reasoning benchmarks, but their performance varies inconsistently across problems with varying levels of difficulty. This paper describes Adaptive Multi-Expert Reasoning…
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical…
Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR…
The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use…
The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical…
This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized…