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This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

Numerical Analysis · Mathematics 2025-07-24 Michał Wichrowski

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…

Numerical Analysis · Mathematics 2022-09-12 Yannis Voet

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…

Computational Engineering, Finance, and Science · Computer Science 2025-06-24 Weihang Ouyang , Yeonjong Shin , Si-Wei Liu , Lu Lu

We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators based on sum factorization on quadrilateral and hexahedral meshes. We identify a set of kernels for fast quadrature on cells…

Mathematical Software · Computer Science 2019-09-11 Martin Kronbichler , Katharina Kormann

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…

Computational Engineering, Finance, and Science · Computer Science 2025-12-02 Shahed Rezaei , Reza Najian Asl , Kianoosh Taghikhani , Ahmad Moeineddin , Michael Kaliske , Markus Apel

The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…

Quantum Physics · Physics 2025-10-22 Ahmad M. Alkadri , Tyler D. Kharazi , K. Birgitta Whaley , Kranthi K. Mandadapu

Mixture-of-Experts (MoE) layers activate a subset of model weights, dubbed experts, to improve model performance. MoE is particularly promising for deployment on process-in-memory (PIM) architectures, because PIM can naturally fit experts…

Hardware Architecture · Computer Science 2026-02-12 Hanyuan Gao , Xiaoxuan Yang

The hybrid-high order (HHO) scheme has many successful applications including linear elasticity as the first step towards computational solid mechanics. The striking advantage is the simplicity among other higher-order nonconforming schemes…

Numerical Analysis · Mathematics 2026-04-10 Carsten Carstensen , Ngoc Tien Tran

Today's computing systems require moving data back-and-forth between computing resources (e.g., CPUs, GPUs, accelerators) and off-chip main memory so that computation can take place on the data. Unfortunately, this data movement is a major…

Hardware Architecture · Computer Science 2022-05-31 Geraldo F. Oliveira , Amirali Boroumand , Saugata Ghose , Juan Gómez-Luna , Onur Mutlu

Fully Homomorphic Encryption (FHE) imposes substantial memory bandwidth demands, presenting significant challenges for efficient hardware acceleration. Near-memory Processing (NMP) has emerged as a promising architectural solution to…

Hardware Architecture · Computer Science 2025-04-01 Shangyi Shi , Husheng Han , Jianan Mu , Xinyao Zheng , Ling Liang , Hang Lu , Zidong Du , Xiaowei Li , Xing Hu , Qi Guo

Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…

Optimization and Control · Mathematics 2015-07-22 Arun L. Gain , Glaucio H. Paulino , Leonardo Duarte , Ivan F. M. Menezes

We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…

Numerical Analysis · Mathematics 2025-12-11 Nils Margenberg , Carolin Mehlmann

In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…

Computational Physics · Physics 2015-05-30 Phani Motamarri , Mrinal Iyer , Jaroslaw Knap , Vikram Gavini

Sequence alignment is a memory bound computation whose performance in modern systems is limited by the memory bandwidth bottleneck. Processing-in-memory architectures alleviate this bottleneck by providing the memory with computing…

Hardware Architecture · Computer Science 2023-03-28 Safaa Diab , Amir Nassereldine , Mohammed Alser , Juan Gómez-Luna , Onur Mutlu , Izzat El Hajj

Processing large-scale graph datasets is computationally intensive and time-consuming. Processor-centric CPU and GPU architectures, commonly used for graph applications, often face bottlenecks caused by extensive data movement between the…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-11 Marzieh Barkhordar , Alireza Tabatabaeian , Mohammad Sadrosadati , Christina Giannoula , Juan Gomez Luna , Izzat El Hajj , Onur Mutlu , Alaa R. Alameldeen

The growing demand for edge computing and AI drives research into analog in-memory computing using memristors, which overcome data movement bottlenecks by computing directly within memory. However, device failures and variations critically…

Emerging Technologies · Computer Science 2025-07-16 Zhicheng Xu , Jiawei Liu , Sitao Huang , Zefan Li , Shengbo Wang , Bo Wen , Ruibin Mao , Mingrui Jiang , Giacomo Pedretti , Jim Ignowski , Kaibin Huang , Can Li

We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…

Numerical Analysis · Mathematics 2025-01-15 Elena Benvenuti , Gianmarco Manzini , Marco Nale , Simone Pizzolato

We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…

Optimization and Control · Mathematics 2019-06-05 Brian Bullins , Richard Peng

In-memory database query processing frequently involves substantial data transfers between the CPU and memory, leading to inefficiencies due to Von Neumann bottleneck. Processing-in-Memory (PIM) architectures offer a viable solution to…

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