Coarse-grained modeling of crystals by the amplitude expansion of the phase-field crystal model: an overview

M Salvalaglio, KR Elder - Modelling and Simulation in Materials …, 2022 - iopscience.iop.org
Comprehensive investigations of crystalline systems often require methods bridging
atomistic and continuum scales. In this context, coarse-grained mesoscale approaches are …

A review on computational modelling of phase-transition problems

H Gomez, M Bures, A Moure - … Transactions of the …, 2019 - royalsocietypublishing.org
Phase-transition problems are ubiquitous in science and engineering. They have been
widely studied via theory, experiments and computations. This paper reviews the main …

[图书][B] Numerical models for differential problems

A Quarteroni, S Quarteroni - 2009 - Springer
Alfio Quarteroni Third Edition Page 1 MS&A – Modeling, Simulation and Applications 16
Numerical Models for Di erential Problems Alfio Quarteroni Third Edition Page 2 MS&A Volume …

Linearly first-and second-order, unconditionally energy stable schemes for the phase field crystal model

X Yang, D Han - Journal of Computational Physics, 2017 - Elsevier
In this paper, we develop a series of linear, unconditionally energy stable numerical
schemes for solving the classical phase field crystal model. The temporal discretizations are …

Stabilized second‐order convex splitting schemes for Cahn–Hilliard models with application to diffuse‐interface tumor‐growth models

X Wu, GJ Van Zwieten… - International journal for …, 2014 - Wiley Online Library
We present unconditionally energy‐stable second‐order time‐accurate schemes for diffuse‐
interface (phase‐field) models; in particular, we consider the Cahn–Hilliard equation and a …

A fully-discrete decoupled finite element method for the conserved Allen–Cahn type phase-field model of three-phase fluid flow system

X Yang, X He - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
In this article, we develop and analyze a novel fully discrete decoupled finite element
method to solve a flow-coupled ternary phase-field model for the system consisting of three …

The variational collocation method

H Gomez, L De Lorenzis - Computer Methods in Applied Mechanics and …, 2016 - Elsevier
We propose the variational collocation method for the numerical solution of partial
differential equations. The conceptual basis is the establishment of a direct connection …

Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics

A Tagliabue, L Dede, A Quarteroni - Computers & Fluids, 2014 - Elsevier
In this paper, we consider the numerical approximation of high order Partial Differential
Equations (PDEs) by means of NURBS-based Isogeometric Analysis (IGA) in the framework …

A mathematical model coupling tumor growth and angiogenesis

J Xu, G Vilanova, H Gomez - PloS one, 2016 - journals.plos.org
We present a mathematical model for vascular tumor growth. We use phase fields to model
cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and …

An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates

A Reali, H Gomez - Computer Methods in Applied Mechanics and …, 2015 - Elsevier
In this paper, IGA collocation methods are for the first time introduced for the solution of thin
structural problems described by the Bernoulli–Euler beam and Kirchhoff plate models. In …