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This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where the fracture evolution is tracked by a phase field variable. The model we consider is a…

Numerical Analysis · Mathematics 2020-02-19 Mats Kirkesæther Brun , Thomas Wick , Inga Berre , Jan Martin Nordbotten , Florin Adrian Radu

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…

Information Theory · Computer Science 2018-06-15 Veit Elser , Ti-Yen Lan , Tamir Bendory

Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…

Numerical Analysis · Mathematics 2025-06-09 Harald Garcke , Robert Nürnberg

We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show…

Materials Science · Physics 2009-10-31 Alain Karma , Wouter-Jan Rappel

In this paper, we propose and analyze an efficient numerical method for the anisotropic phase field dendritic crystal growth model, which is challenging because we are facing the nonlinear coupling and anisotropic coefficient in the model.…

Numerical Analysis · Mathematics 2023-10-17 Yayu Guo , Mejdi Azaiez , Chuanju Xu

The high computational cost of phase field simulations remains a major limitation for predicting dendritic solidification in metals, particularly in additive manufacturing, where microstructural control is critical. This work presents a…

Even though our theoretical understanding of dendritic solidification is relatively well developed, our current ability to model this process quantitatively remains extremely limited. This is due to the fact that the morphological…

Materials Science · Physics 2007-05-23 Jean Bragard , Alain Karma , Youngyih H. Lee , Mathis Plapp

A new phase field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model's thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al (Phys…

Materials Science · Physics 2008-10-29 Michael Greenwood , Jeffrey J. Hoyt , Nikolas Provatas

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu…

Materials Science · Physics 2026-04-30 Jiefu Tian , David Montiel , Kaihua Ji , Trevor Lyons , Jason Landini , Katsuyo Thornton , Alain Karma

Engineering alloys generally exhibit multi-phase microstructures. For simulating their microstructure evolution during solid-state phase transformation, CALPHAD-guided multi-phase-field models coupled with micro-mechanics have proven to be…

Materials Science · Physics 2023-01-05 Sourav Chatterjee , Daniel Schwen , Nele Moelans

We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…

Numerical Analysis · Mathematics 2023-07-06 Mathias Anselmann , Markus Bause , Nils Margenberg , Pavel Shamko

We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…

Numerical Analysis · Mathematics 2020-10-14 Aleš Wodecki , Pavel Strachota , Michal Beneš

In functionally graded materials (FGMs) fabricated using directed energy deposition (DED) additive manufacturing (AM), cracks may form due to interdendritic stress during solidification, the formation of intermetallics, or the buildup of…

Materials Science · Physics 2023-05-22 Zhening Yang , Hui Sun , Zi-Kui Liu , Allison M. Beese

Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance…

Machine Learning · Computer Science 2026-03-17 Karim K. Ben Hicham , Moreno Ascani , Jan G. Rittig , Alexander Mitsos

A general model is formulated for elasto-plastic materials undergoing linear kinematic hardening to describe microstructure evolution associated with phase transformations. Using infinitesimal strain theory, the model is based on…

Computational Engineering, Finance, and Science · Computer Science 2026-02-20 Sarah Dinkelacker-Steinhoff , Klaus Hackl

Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…

Optimization and Control · Mathematics 2020-11-13 Yoshihiro Kanno

We present a first implementation of the Dendritic Needle Network (DNN) model for dendritic crystal growth in three dimensions including convective transport in the melt. The numerical solving of the Navier-Stokes equations is performed…

Computational Physics · Physics 2020-06-18 Thomas Isensee , Damien Tourret

Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…

Computational Physics · Physics 2021-02-19 K. Tůma , M. Rezaee-Hajidehi , J. Hron , P. E. Farrell , S. Stupkiewicz

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…

Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…

Optimization and Control · Mathematics 2022-01-14 Marc Goerigk , Mohammad Khosravi