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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

This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…

Numerical Analysis · Mathematics 2022-09-02 Shuhao Cao , Long Chen , Ruchi Guo , Frank Lin

This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…

Computational Geometry · Computer Science 2025-08-08 Lei Shangyu , Fan Wei , Ren Hui

In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method…

Numerical Analysis · Mathematics 2019-09-04 Shubin Fu , Eric Chung , Guanglian Li

We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…

Computational Geometry · Computer Science 2017-11-20 J. M. Taramón , J. P. Morgan , C. Shi , J. Hasenclever

In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…

Numerical Analysis · Mathematics 2017-02-13 Maxim A. Olshanskii , Xianmin Xu

This paper proposes two contributions to the calculation of free surface flows using the particle finite element method (PFEM). The PFEM is based on a Lagrangian approach: a set of particles defines the fluid. Then, unlike a pure Lagrangian…

Computational Engineering, Finance, and Science · Computer Science 2025-01-08 Thomas Leyssens , Michel Henry , Jonathan Lambrechts , Jean-Francois Remacle

This paper is dedicated to the rigorous numerical analysis of a Multiscale Finite Element Method (MsFEM) for the Stokes system, when dealing with highly heterogeneous media, as proposed in [B.P.~Muljadi et al., arXiv:1404.2837]. The method…

Numerical Analysis · Mathematics 2018-02-14 Gaspard Jankowiak , Alexei Lozinski

This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…

Numerical Analysis · Mathematics 2022-12-05 Mathias Schmidt , Lise Noel , Keenan Doble , John A. Evans , Kurt Maute

In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…

Numerical Analysis · Mathematics 2022-09-14 Kuokuo Zhang , Weibing Deng , Haijun Wu

We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated…

Computational Engineering, Finance, and Science · Computer Science 2021-06-03 Yu-Hsiang Lan , Paul Fischer , Elia Merzari , Misun Min

We present a virtual element method (VEM) for the numerical approximation of the electromagnetics subsystem of the resistive magnetohydrodynamics (MHD) model in two spatial dimensions. The major advantages of the virtual element method…

Numerical Analysis · Mathematics 2020-04-27 S. Naranjo Alvarez , V. A. Bokil , V. Gyrya , G. Manzini

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle-mesh frictional contact using a variational time-stepping…

Numerical Analysis · Mathematics 2022-02-02 Xuan Li , Yu Fang , Minchen Li , Chenfanfu Jiang

In this work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, and allows us to construct novel discretizations for…

Numerical Analysis · Mathematics 2021-04-12 Sebastian Naranjo-Alvarez , Vrushali Bokil , Vitaliy Gyrya , Gianmarco Manzini

We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [59] the problem is supposed to have a unique solution, but…

Numerical Analysis · Mathematics 2014-12-09 L. Beirão da Veiga , F. Brezzi , L. D. Marini , A. Russo

In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…

Numerical Analysis · Mathematics 2020-07-20 Zhengkang He , Eric T. Chung , Jie Chen , Zhangxin Chen

The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation…

Numerical Analysis · Mathematics 2015-01-16 Maxim A. Olshanskii , Danil Safin

The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…

The objective of this article is to address the discretisation of fractured/faulted poromechanical models using 3D polyhedral meshes in order to cope with the geometrical complexity of faulted geological models. A polytopal scheme is…

Numerical Analysis · Mathematics 2024-03-20 Jérôme Droniou , Guillaume Enchéry , Isabelle Faille , Ali Haidar , Roland Masson

To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…

Applied Physics · Physics 2026-04-07 Hongxin Wang , Jie Liu , Guilin Wen