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I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…
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…
In this article, we present a novel approach for block-structured adaptive mesh refinement (AMR) that is suitable for extreme-scale parallelism. All data structures are designed such that the size of the meta data in each distributed…
This paper examines the application of adaptive mesh refinement (AMR) in the field of numerical weather prediction (NWP). We implement and assess two distinct AMR approaches and evaluate their performance through standard NWP benchmarks. In…
Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of ECP applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion,…
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…
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…
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,…
High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual…
Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…
Sparse rewards are a major bottleneck in multi-agent reinforcement learning (MARL), where simultaneous learning induces non-stationarity and makes reward design especially delicate. Reward shaping can accelerate learning, but in the…
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…
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…
We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial…
This paper presents novel refinement sensors for the application to adaptive mesh and algorithm refinement (AMAR) with kinetic models, such as discrete velocity and lattice Boltzmann methods. While refinement criteria for AMAR based on…
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…
Reasoning about failures is crucial for building reliable and trustworthy robotic systems. Prior approaches either treat failure reasoning as a closed-set classification problem or assume access to ample human annotations. Failures in the…
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 advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…
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,…