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The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…

Numerical Analysis · Mathematics 2015-04-21 Annalisa Buffa , Carlotta Giannelli

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-08 Anjiang Wei , Hang Song , Mert Hidayetoglu , Elliott Slaughter , Sanjiva K. Lele , Alex Aiken

Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…

Computational Engineering, Finance, and Science · Computer Science 2022-07-18 Chennakesava Kadapa , Xinyu Wang , Yue Mei

This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

Optimization and Control · Mathematics 2020-04-22 Shanglong Zhang , Arun L. Gain , Julian A. Norato

Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved…

Machine Learning · Computer Science 2026-02-04 Jiangyong Yu , Xiaomeng Han , Xing Hu , Chen Xu , Zhe Jiang , Dawei Yang

Large language models (LLMs) have enabled the creation of multi-modal LLMs that exhibit strong comprehension of visual data such as images and videos. However, these models usually rely on extensive visual tokens from visual encoders,…

Computer Vision and Pattern Recognition · Computer Science 2025-07-30 Yiwu Zhong , Zhuoming Liu , Yin Li , Liwei Wang

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…

Instrumentation and Methods for Astrophysics · Physics 2020-07-08 James M. Stone , Kengo Tomida , Christopher J. White , Kyle G. Felker

Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive…

Computational Engineering, Finance, and Science · Computer Science 2021-07-13 Shashwat Sharma , Piero Triverio

We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to…

Atmospheric and Oceanic Physics · Physics 2025-08-27 Giuseppe Orlando , Tommaso Benacchio , Luca Bonaventura

Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The…

Fluid Dynamics · Physics 2022-03-14 Aaron B. Buhendwa , Deniz A. Bezgin , Nikolaus Adams

The evolution of parallel I/O library as well as new concepts such as 'in transit' and 'in situ' visualization and analysis have been identified as key technologies to circumvent I/O bottleneck in pre-exascale applications. Nevertheless,…

Instrumentation and Methods for Astrophysics · Physics 2022-09-13 Loïc Strafella , Damien Chapon

This letter proposes a fluid reconfigurable intelligent surface (FRIS) paradigm, extending the conventional reconfigurable intelligent surface (RIS) technology to incorporate position reconfigurability of the elements. In our model, a…

Information Theory · Computer Science 2025-03-20 Han Xiao , Xiaoyan Hu , Kai-Kit Wong , Hanjiang Hong , George C. Alexandropoulos , Chan-Byoung Chae

Efficient AI inference on AMD's Versal AI Engine (AIE) is challenging due to tightly coupled VLIW execution, explicit datapaths, and local memory management. Prior work focused on first-generation AIE kernel optimizations, without tackling…

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the…

Astrophysics · Physics 2008-11-26 Francesco Miniati , Phillip Colella

We present a GPU-native mesh adaptation procedure that incorporates a complex geometry represented with a triangle mesh within a primary Cartesian computational grid organized as a forest of octrees. A C++/CUDA program implements the…

Computational Geometry · Computer Science 2025-02-25 Khodr Jaber , Ebenezer E. Essel , Pierre E. Sullivan

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…

Numerical Analysis · Mathematics 2010-09-28 Shun Wang , Eric de Sturler , Glaucio H. Paulino

It has been observed that deep neural networks (DNNs) often use both genuine as well as spurious features. In this work, we propose "Amending Inherent Interpretability via Self-Supervised Masking" (AIM), a simple yet interestingly effective…

Computer Vision and Pattern Recognition · Computer Science 2025-08-18 Eyad Alshami , Shashank Agnihotri , Bernt Schiele , Margret Keuper

This paper aims to provide a machine learning framework to simulate two-phase flow in porous media. The proposed algorithm is based on Physics-informed neural networks (PINN). A novel residual-based adaptive PINN is developed and compared…

Numerical Analysis · Mathematics 2022-06-01 John M. Hanna , Jose V. Aguado , Sebastien Comas-Cardona , Ramzi Askri , Domenico Borzacchiello

We push the boundaries of electronic structure-based \textit{ab-initio} molecular dynamics (AIMD) beyond 100 million atoms. This scale is otherwise barely reachable with classical force-field methods or novel neural network and machine…

We extend the entropy-stable oscillation-eliminating discontinuous Galerkin spectral element method (ES-OEDG) on curvilinear meshes to adaptive mesh refinement (AMR) grids with nonconforming interfaces. The formulation targets…

Numerical Analysis · Mathematics 2026-04-24 Jieling Yang , Guosheng Fu