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SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software's sustainability. In this publication we solve this sustainability and…

Numerical Analysis · Mathematics 2018-12-20 Dominic Kempf , René Heß , Steffen Müthing , Peter Bastian

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…

Numerical Analysis · Mathematics 2026-01-14 Yanpeng Gong , Sishuai Li , Yue Mei , Bingbing Xu , Fei Qin , Xiaoying Zhuang , Timon Rabczuk

One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…

Machine Learning · Computer Science 2024-04-29 Theresa Wagner , Franziska Nestler , Martin Stoll

Numerical methods such as the Finite Element Method (FEM) have been successfully adapted to utilize the computational power of GPU accelerators. However, much of the effort around applying FEM to GPU's has been focused on high-order FEM due…

We present a differentiable weak-form learning approach for accelerating finite element simulations. Rather than introducing black-box source terms in the strong form of the governing equations, we augment the momentum equation directly in…

Fluid Dynamics · Physics 2026-01-29 Junoh Jung , Emil Constantinescu

Vectorization is a compiler optimization that replaces multiple operations on scalar values with a single operation on vector values. Although common in traditional compilers such as rustc, clang, and gcc, vectorization is not common in the…

This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…

Numerical Analysis · Mathematics 2020-02-10 M. Cihan , F. Aldakheel , B. Hudobivnik , P. Wriggers

Finite-element (FE) discretisations have emerged as a powerful real-space alternative to large-scale Kohn-Sham density functional theory (DFT) calculations, offering systematic convergence, excellent parallel scalability, while…

Computational Physics · Physics 2025-12-11 Gourab Panigrahi , Phani Motamarri

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

The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…

Computational Physics · Physics 2023-07-25 Alexander Chervyakov

Much of the current focus in high-performance computing is on multi-threading, multi-computing, and graphics processing unit (GPU) computing. However, vectorization and non-parallel optimization techniques, which can often be employed…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-18 Neil G. Dickson , Kamran Karimi , Firas Hamze

Three-dimensional concrete printing (3DCP) has gained a lot of popularity in recent years. According to many, 3DCP is set to revolutionize the construction industry: yielding unparalleled aesthetics, better quality control, lower cost, and…

Computational Physics · Physics 2020-09-16 Gieljan Vantyghem , Ticho Ooms , Wouter De Corte

This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…

Numerical Analysis · Mathematics 2025-12-29 Yanpeng Gong , Sishuai Li , Fei Qin , Bingbing Xu

In this work, a recently developed fracture modeling method called localizing gradient damage method (LGDM) is implemented in MATLAB. MATLAB is well-known in the computational research community for its simple and easy-to-learn coding…

Numerical Analysis · Mathematics 2023-01-18 Subrato Sarkar

Matrix-free finite element implementations of massively parallel geometric multigrid save memory and are often significantly faster than implementations using classical sparse matrix techniques. They are especially well suited for…

Numerical Analysis · Mathematics 2016-08-24 Simon Bauer , Marcus Mohr , Ulrich Rüde , Jens Weismüller , Markus Wittmann , Barbara Wohlmuth

An extremely fast time-harmonic finite element solver developed for the transmission analysis of photonic crystals was applied to mask simulation problems. The applicability was proven by examining a set of typical problems and by a…

Optics · Physics 2009-05-28 S. Burger , R. Köhle , L. Zschiedrich , W. Gao , F. Schmidt , R. März , C. Nölscher

In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…

Optics · Physics 2024-09-12 Jingwei Wang , Lida Liu , Yuhao Jing , Zhongfei Xiong , Yuntian Chen

This work describes and demonstrates the operation of a virtual X-ray algorithm operating on finite-element post-processing results which allows for higher polynomial orders in geometry representation as well as density distribution. A…

Computational Engineering, Finance, and Science · Computer Science 2021-05-07 Maximilian Bittens

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…

Quantum Physics · Physics 2025-04-01 Abhishek Arora , Benjamin M. Ward , Caglar Oskay

We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces…

Numerical Analysis · Computer Science 2018-07-24 Simon Bauer , Daniel Drzisga , Marcus Mohr , Ulrich Ruede , Christian Waluga , Barbara Wohlmuth