English
Related papers

Related papers: A Rigorous Finite-Element Domain Decomposition Met…

200 papers

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

Numerical Analysis · Mathematics 2023-08-08 Efthymios N. Karatzas , Francesco Ballarin , Gianluigi Rozza

Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient…

Numerical Analysis · Mathematics 2019-11-18 Helmut Harbrecht , Marc Schmidlin

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational…

We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…

Numerical Analysis · Mathematics 2020-12-08 Michel Duprez , Vanessa Lleras , Alexei Lozinski

Present day electromagnetic field calculations have limitations that are due to techniques employing edge-based discretization methods. While these vector finite element methods solve the issues of tangential continuity of fields and the…

Computational Physics · Physics 2019-12-11 Dung N. Pham , Sathwik Bharadwaj , L. R. Ram-Mohan

This paper proposes a fast time-domain boundary element method (TDBEM) to solve three-dimensional transient electromagnetic scattering problems regarding perfectly electric conductors in the classical marching-on-in-time manner. The…

Computational Physics · Physics 2023-03-10 Toru Takahashi

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Machine Learning · Computer Science 2021-09-21 Alban Odot , Ryadh Haferssas , Stéphane Cotin

Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive…

Numerical Analysis · Mathematics 2025-10-28 Gareth Hardwick , Haizhao Yang

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…

Numerical Analysis · Mathematics 2024-03-18 Stefano Berrone , Fabio Vicini

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…

Numerical Analysis · Mathematics 2024-09-26 Ionut-Gabriel Farcas , Rayomand P. Gundevia , Ramakanth Munipalli , Karen E. Willcox

Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…

Graphics · Computer Science 2018-07-04 Silvia Sellán , Herng Yi Cheng , Yuming Ma , Mitchell Dembowski , Alec Jacobson

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

Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…

Numerical Analysis · Mathematics 2011-07-26 Sundararajan Natarajan , D. Roy Mahapatra , Stephane PA Bordas

This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…

Numerical Analysis · Mathematics 2021-11-09 Fucheng Tian , Xiaoliang Tang , Tingyu Xu , Liangbin Li

We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…

Optics · Physics 2026-04-15 Ergun Simsek

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

The propagation of sound waves in a horizontally stratified environment, a classic problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the…

Computational Engineering, Finance, and Science · Computer Science 2021-07-29 Houwang Tu , Yongxian Wang , Qiang Lan , Wei Liu , Wenbin Xiao , Shuqing Ma

We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks. The field solution on each…

Numerical Analysis · Mathematics 2021-09-22 Suchuan Dong , Zongwei Li

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

Numerical Analysis · Mathematics 2026-02-10 Yuming Ba , Liang Chen , Yaru Chen , Qiuqi Li

In the literature about field emission, finite elements and finite differences techniques are being increasingly employed to understand the local field enhancement factor (FEF) via numerical simulations. In theoretical analyses, it is usual…

Computational Physics · Physics 2023-05-03 Thiago A. de Assis , Fernando F. Dall'Agnol