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We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…

计算工程、金融与科学 · 计算机科学 2022-05-18 Rishith Ellath Meethal , Birgit Obst , Mohamed Khalil , Aditya Ghantasala , Anoop Kodakkal , Kai-Uwe Bletzinger , Roland Wüchner

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…

数值分析 · 数学 2023-10-31 Hauke Gravenkamp , Albert A. Saputra , Sascha Eisenträger

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

数值分析 · 数学 2018-11-07 Nicola Demo , Marco Tezzele , Gianluca Gustin , Gianpiero Lavini , Gianluigi Rozza

We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…

最优化与控制 · 数学 2019-07-12 Tommy Etling , Roland Herzog , Estefanía Loayza , Gerd Wachsmuth

The combination of Finite Element Method (FEM) simulation and experimental photo-elasticity provides both qualitative and quantitative information about the stress field in a polymer composite and particularly along the fibre-matrix…

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…

光学 · 物理学 2009-05-28 L. Zschiedrich , S. Burger , A. Schädle , F. Schmidt

The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…

数值分析 · 数学 2025-10-02 Lefu Cai , Zhixin Liu , Minghui Song , Xianchao Wang

Endovascular aneurysm repair (EVAR) is a current alternative treatment for thoracic and abdominal aortic aneurysms, but is still sometimes compromised by possible complications such as device migration or endoleaks. In order to assist…

医学物理 · 物理学 2019-02-05 V. Acosta Santamaría , G. Daniel , D. Perrin , J. Albertini , E. Rosset , S. Avril

Sintering of printed porcelain filaments can be strongly affected by overhang geometry, thin features, and printing-induced anisotropy. These effects are particularly difficult to simulate because they require accurately capturing the…

经典物理 · 物理学 2025-12-03 Fatima Hammoud , Charles Manière

In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…

光学 · 物理学 2024-12-03 Fan Xiao , Jingwei Wang , Zhongfei Xiong , Yuntian Chen

Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into…

计算工程、金融与科学 · 计算机科学 2025-08-20 Tan Tran , Denisa Martonova , Sigrid Leyendecker

Electromagnetic forming and perforations (EMFP) are complex and innovative high strain rate processes that involve electromagnetic-mechanical interactions for simultaneous metal forming and perforations. Instead of spending costly resources…

数值分析 · 数学 2024-12-16 Avinash Chetry , Arup Nandy

Background: Mammography is a specific type of breast imaging that uses low-dose X-rays to detect cancer in early stage. During the exam, the women breast is compressed between two plates in order to even out the breast thickness and to…

医学物理 · 物理学 2018-11-27 Anna Mîra , Ann-Katherine Carton , Serge Muller , Yohan Payan

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…

计算物理 · 物理学 2012-02-20 J. E. Sprittles , Y. D. Shikhmurzaev

Heat transfer in the human eyeball, a complex organ, is significantly influenced by various pathophysiological and external parameters. Particularly, heat transfer critically affects fluid behavior within the eye and ocular drug delivery…

偏微分方程分析 · 数学 2024-10-14 Thomas Saigre , Christophe Prud'Homme , Marcela Szopos

The Finite Element Method (FEM) is a powerful modeling tool for predicting soft robots' behavior, but its computation time can limit practical applications. In this paper, a learning-based approach based on condensation of the FEM model is…

机器人学 · 计算机科学 2025-03-20 Etienne Ménager , Tanguy Navez , Paul Chaillou , Olivier Goury , Alexandre Kruszewski , Christian Duriez

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used…

光学 · 物理学 2007-09-25 S. Burger , L. Zschiedrich , F. Schmidt , R. Köhle , T. Henkel , B. Küchler , C. Nölscher

In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In…

We discuss realization, properties and performance of the adaptive finite element approach to the design of nano-photonic components. Central issues are the construction of vectorial finite elements and the embedding of bounded components…

光学 · 物理学 2015-05-13 Jan Pomplun , Sven Burger , Lin Zschiedrich , Frank Schmidt

Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities,…

计算工程、金融与科学 · 计算机科学 2021-02-24 Maria Girardi , Cristina Padovani , Daniele Pellegrini , Leonardo Robol