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The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. This method uses a finite element (FE) method to approximate the stresses and forces…

Numerical Analysis · Mathematics 2023-02-01 David Wells , Ben Vadala-Roth , Jae H. Lee , Boyce E. Griffith

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…

Numerical Analysis · Computer Science 2011-07-20 Stephane PA Bordas , Sundararajan Natarajan

We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…

Numerical Analysis · Mathematics 2012-05-22 Lijian Jiang , Dylan Copeland , J. David Moulton

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

Numerical Analysis · Mathematics 2013-04-30 Zhu Wang

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…

Numerical Analysis · Mathematics 2014-07-02 Victor Calo , Yalchin Efendiev , Juan Galvis , Mehdi Ghommem

A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses,…

Computational Physics · Physics 2020-03-31 M. Amir Siddiq

This paper presents an extension of the discrete element method using a phase-field formulation to incorporate grain shape and its evolution. The introduction of a phase variable enables an effective representation of grain geometry and…

Materials Science · Physics 2024-04-09 Alexandre Sac-Morane , Manolis Veveakis , Hadrien Rattez

This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…

We establish a simple, rigorous, and easy to implement connection between the classical continuous finite element method (FEM) and the discontinuous Galerkin (DG) method for Poisson's problem. The key idea is to insert a vanishing-thickness…

The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…

Numerical Analysis · Mathematics 2022-01-10 Marcelo Forets , Daniel Freire Caporale , Jorge M. Pérez Zerpa

Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…

Numerical Analysis · Mathematics 2025-06-19 Jennifer E. Fromm , John A. Evans , J. S. Chen

This paper presents the implementation of the eXtended Finite Element Method (XFEM) in the general-purpose commercial software package COMSOL Multiphysics for multi-field thermo-hydro-mechanical problems in discontinuous porous media. To…

Mathematical Software · Computer Science 2021-12-23 Ahmad Jafari , Mohammad Vahab , Pooyan Broumand , Nasser Khalili

In this paper, we replace the asymptotic enrichments around the crack tip in the extended finite element method (XFEM) with the semi-analytical solution obtained by the scaled boundary finite element method (SBFEM). The proposed method does…

Numerical Analysis · Mathematics 2013-09-04 Sundararajan Natarajan , Chongmin Song

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…

Numerical Analysis · Mathematics 2014-03-04 Joerg Grande , Maxim Olshanskii , Arnold Reusken

In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…

Numerical Analysis · Mathematics 2025-05-06 Tianlong He , Philippe Karamian-Surville , Daniel Choï

In this work, the finite elements method (FEM) is used to analyse the growth of fretting cracks. FEM can be favourably used to extract the stress intensity factors in mixed mode, a typical situation for cracks growing in the vicinity of a…

Geophysics · Physics 2011-02-24 Henry Proudhon , Stéphanie Basseville

In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…

Numerical Analysis · Mathematics 2024-11-27 Antoine Quiriny , Václav Kučera , Jonathan Lambrechts , Nicolas Moës , Jean-François Remacle

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…

Numerical Analysis · Mathematics 2021-04-07 Matteo Cusini , Joshua A. White , Nicola Castelletto , Randolph R. Settgast

We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…

Numerical Analysis · Mathematics 2023-01-25 Jennifer E. Fromm , Nils Wunsch , Ru Xiang , Han Zhao , Kurt Maute , John A. Evans , David Kamensky

In this paper, we extend the recently proposed extended scaled boundary finite element method (xSBFEM)~\cite{natarajansong2013} to study fracture parameters of interfacial cracks and cracks terminating at the interface. The approach is also…

Numerical Analysis · Mathematics 2014-07-14 Sundararajan Natarajan , Chongmin Song , Salim Belouettar