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Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-05 Scott Sallinen , Abdullah Gharaibeh , Matei Ripeanu

The mixture-of-experts (MoE) architecture scales model size with sublinear computational increase but suffers from memory-intensive inference due to KV caches and sparse expert activation. Recent disaggregated expert parallelism (DEP)…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-12-29 Xinglin Pan , Shaohuai Shi , Wenxiang Lin , Yuxin Wang , Zhenheng Tang , Wei Wang , Xiaowen Chu

MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…

This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…

Numerical Analysis · Mathematics 2022-04-12 Peter Munch , Timo Heister , Laura Prieto Saavedra , Martin Kronbichler

This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…

Computational Engineering, Finance, and Science · Computer Science 2025-08-04 Yuxi Xie , Ethan J. Wu , Lu Xu , Jimmy Perez , Shaofan Li

Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-06-30 Yuanhang Yu , Dong Wen , Ying Zhang , Xiaoyang Wang , Wenjie Zhang , Xuemin Lin

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

In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…

Computational Physics · Physics 2026-02-18 F. Şık , F. L. Teixeira , B. Shanker

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…

Numerical Analysis · Computer Science 2017-06-06 T. P. Fries

In this paper we present a new GPU-oriented mesh optimization method based on high-order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global…

Mathematical Software · Computer Science 2022-12-28 Jean-Sylvain Camier , Veselin Dobrev , Patrick Knupp , Tzanio Kolev , Ketan Mittal , Robert Rieben , Vladimir Tomov

Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…

Numerical Analysis · Mathematics 2019-07-24 Peter Bastian , Eike Hermann Müller , Steffen Müthing , Marian Piatkowski

Edge computing has become increasingly popular across many domains and enterprises. However, given the locality constraint of edges (i.e., only close-by edges are useful), multiplexing diverse workloads becomes challenging. This results in…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-26 Faria Kalim , Shadi A. Noghabi

Neural architecture search (NAS) is a challenging problem. Hierarchical search spaces allow for cheap evaluations of neural network sub modules to serve as surrogate for architecture evaluations. Yet, sometimes the hierarchy is too…

Neural and Evolutionary Computing · Computer Science 2024-04-26 Simon Neumeyer , Julian Stier , Michael Granitzer

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-06-27 Christoph Lehrenfeld , Arnold Reusken

The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element…

Mathematical Software · Computer Science 2016-10-07 Lawrence Mitchell , Eike Hermann Müller

Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over…

Mathematical Software · Computer Science 2020-08-26 Tianjiao Sun , Lawrence Mitchell , Kaushik Kulkarni , Andreas Klöckner , David A. Ham , Paul H. J. Kelly

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

The rapid development of parallel and distributed computing paradigms has brought about great revolution in computing. Thanks to the intrinsic parallelism of evolutionary computation (EC), it is natural to implement EC on parallel and…

Neural and Evolutionary Computing · Computer Science 2023-04-13 Wei-Neng Chen , Feng-Feng Wei , Tian-Fang Zhao , Kay Chen Tan , Jun Zhang

This work investigates a variant of the conjugate gradient (CG) method and embeds it into the context of high-order finite-element schemes with fast matrix-free operator evaluation and cheap preconditioners like the matrix diagonal. Relying…

Mathematical Software · Computer Science 2022-05-19 Martin Kronbichler , Dmytro Sashko , Peter Munch

Dataset condensation, a concept within data-centric learning, efficiently transfers critical attributes from an original dataset to a synthetic version, maintaining both diversity and realism. This approach significantly improves model…

Machine Learning · Computer Science 2025-01-20 Shitong Shao , Zikai Zhou , Huanran Chen , Zhiqiang Shen