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In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…

Numerical Analysis · Mathematics 2021-09-30 Santiago Badia , Alberto F. Martín , Eric Neiva , Francesc Verdugo

We present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff-Love thin shell theory using a curvilinear surface description. All kinematical objects…

Computational Engineering, Finance, and Science · Computer Science 2020-06-19 Karsten Paul , Christopher Zimmermann , Kranthi K. Mandadapu , Thomas J. R. Hughes , Chad M. Landis , Roger A. Sauer

This article focuses on the finite volume method (FVM) as an instrument tool to deal with the non-linear collisional-induced breakage equation (CBE) that arises in the particulate process. Notably, we consider the non-conservative…

Numerical Analysis · Mathematics 2024-11-27 Sanjiv Kumar Bariwal , Rajesh Kumar

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

We propose a variational phase-field model of fracture capable of accounting for arbitrary closed convex strength domains. Unlike traditional models based on Ambrosio and Tortorelli regularization, the phase-field variable does not affect…

Applied Physics · Physics 2025-07-01 Blaise Bourdin , Jean-Jacques Marigo , Corrado Maurini , Camilla Zolesi

This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…

Numerical Analysis · Mathematics 2026-03-19 Hou Man , Chongmin Song , Sundararajan Natarajan , Ean Tat Ooi , Carolin Birk

While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…

Computational Engineering, Finance, and Science · Computer Science 2020-08-13 Hyoung Suk Suh , WaiChing Sun , Devin O'Connor

This work presents a new adaptive approach for the numerical simulation of a phase-field model for fractures in nearly incompressible solids. In order to cope with locking effects, we use a recently proposed mixed form where we have a…

Numerical Analysis · Mathematics 2021-06-18 Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical foundations established in the first two parts, which included a…

Analysis of PDEs · Mathematics 2025-07-31 Roberto Alessi , Francesco Colasanto , Matteo Focardi

A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation…

Materials Science · Physics 2020-06-04 P. Carrara , M. Ambati , R. Alessi , L. De Lorenzis

The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM uses the so-called hybrid-dimensional approach to treat fractures explicitly as low-dimensional entries (e.g.…

Numerical Analysis · Mathematics 2021-02-01 Ziyao Xu , Yang Yang

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…

Numerical Analysis · Mathematics 2014-03-21 Klaus Deckelnick , Charles M. Elliott , Thomas Ranner

We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…

Numerical Analysis · Mathematics 2018-08-28 August Johansson , Benjamin Kehlet , Mats G. Larson , Anders Logg

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

In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…

Materials Science · Physics 2011-11-08 J. Novák , Ł. Kaczmarczyk , P. Grassl , J. Zeman , C. J. Pearce

The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…

Materials Science · Physics 2026-01-01 Juan Michael Sargado , Joachim Mathiesen

This paper presents several test cases intended to be benchmarks for numerical schemes for single-phase fluid flow in fractured porous media. A number of solution strategies are compared, including a vertex and a cell-centered finite volume…

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…

Numerical Analysis · Mathematics 2023-06-28 Wenyu Lei , George Turkiyyah , Omar Knio

A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly…

Numerical Analysis · Mathematics 2019-09-04 Emmanouil Kakouris , Savvas P. Triantafyllou

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

Numerical Analysis · Mathematics 2017-10-24 Yujie Liu , Junping Wang , Qingsong Zou